% Mizar problem: t213_xcmplx_1,xcmplx_1,1490,21 
fof(t213_xcmplx_1, conjecture,  (! [A] :  (v1_xcmplx_0(A) =>  (! [B] :  (v1_xcmplx_0(B) => k5_xcmplx_0(k7_xcmplx_0(A, B))=k7_xcmplx_0(B, A)) ) ) ) ).
fof(involutiveness_k5_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => k5_xcmplx_0(k5_xcmplx_0(A))=A) ) ).
fof(dt_k5_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_xcmplx_0(k5_xcmplx_0(A))) ) ).
fof(dt_k7_xcmplx_0, axiom, $true).
fof(fc5_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => v1_xcmplx_0(k7_xcmplx_0(A, B))) ) ).
fof(rc1_xcmplx_0, axiom,  (? [A] : v1_xcmplx_0(A)) ).
fof(rc2_xcmplx_0, axiom,  (? [A] : v1_xcmplx_0(A)) ).
fof(spc11_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k7_xcmplx_0(k5_xcmplx_0(A), k5_xcmplx_0(B))=k7_xcmplx_0(B, A)) ) ).
fof(l58_xcmplx_1, axiom,  (! [A] :  (v1_xcmplx_0(A) =>  (! [B] :  (v1_xcmplx_0(B) => k5_xcmplx_0(k7_xcmplx_0(A, B))=k7_xcmplx_0(B, A)) ) ) ) ).
