% Mizar problem: t7_card_2,card_2,519,5 
fof(t7_card_2, conjecture,  (! [A] :  (! [B] :  (r2_wellord2(k2_zfmisc_1(A, B), k2_zfmisc_1(k1_card_1(A), B)) &  (r2_wellord2(k2_zfmisc_1(A, B), k2_zfmisc_1(A, k1_card_1(B))) &  (r2_wellord2(k2_zfmisc_1(A, B), k2_zfmisc_1(k1_card_1(A), k1_card_1(B))) &  (k1_card_1(k2_zfmisc_1(A, B))=k1_card_1(k2_zfmisc_1(k1_card_1(A), B)) &  (k1_card_1(k2_zfmisc_1(A, B))=k1_card_1(k2_zfmisc_1(A, k1_card_1(B))) & k1_card_1(k2_zfmisc_1(A, B))=k1_card_1(k2_zfmisc_1(k1_card_1(A), k1_card_1(B)))) ) ) ) ) ) ) ).
fof(cc1_card_1, axiom,  (! [A] :  (v1_card_1(A) => v3_ordinal1(A)) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(A)) ) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(A)) ) ).
fof(dt_k1_card_1, axiom,  (! [A] : v1_card_1(k1_card_1(A))) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
fof(l11_card_2, axiom,  (! [A] :  (! [B] : r2_wellord2(k2_zfmisc_1(A, B), k2_zfmisc_1(k1_card_1(A), B))) ) ).
fof(l5_card_2, axiom,  (! [A] :  (! [B] :  (r2_wellord2(k2_zfmisc_1(A, B), k2_zfmisc_1(B, A)) & k1_card_1(k2_zfmisc_1(A, B))=k1_card_1(k2_zfmisc_1(B, A))) ) ) ).
fof(projectivity_k1_card_1, axiom,  (! [A] : k1_card_1(k1_card_1(A))=k1_card_1(A)) ).
fof(rc1_card_1, axiom,  (? [A] : v1_card_1(A)) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rd1_card_1, axiom,  (! [A] :  (v1_card_1(A) => k1_card_1(A)=A) ) ).
fof(redefinition_r2_wellord2, axiom,  (! [A, B] :  (r2_wellord2(A, B) <=> r3_tarski(A, B)) ) ).
fof(reflexivity_r2_wellord2, axiom,  (! [A, B] : r2_wellord2(A, A)) ).
fof(symmetry_r2_wellord2, axiom,  (! [A, B] :  (r2_wellord2(A, B) => r2_wellord2(B, A)) ) ).
fof(t15_wellord2, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_wellord2(A, B) & r2_wellord2(B, C))  => r2_wellord2(A, C)) ) ) ) ).
fof(t5_card_1, axiom,  (! [A] :  (! [B] :  (r2_wellord2(A, B) <=> k1_card_1(A)=k1_card_1(B)) ) ) ).
