eqtr

Theorem.

Arguments:

a (obj), b (obj), c (obj),

Assertions:

((aeqb)to((beqc)to(aeqc)))

Proof:

Hyp Ref Line Expr
df-equ1((aeqb)to((aleb)wedge(blea)))
1siman<2((aeqb)to(aleb))
df-equ3((beqc)to((blec)wedge(cleb)))
3siman<4((beqc)to(blec))
2, 4im.bldan<>5(((aeqb)wedge(beqc))to((aleb)wedge(blec)))
5tr-an6(((aeqb)wedge(beqc))to(alec))
1siman>7((aeqb)to(blea))
3siman>8((beqc)to(cleb))
7, 8im.bldan<>9(((aeqb)wedge(beqc))to((blea)wedge(cleb)))
9ancom10(((aeqb)wedge(beqc))to((cleb)wedge(blea)))
10tr-an11(((aeqb)wedge(beqc))to(clea))
6, 11jca12(((aeqb)wedge(beqc))to((alec)wedge(clea)))
12df-equ13(((aeqb)wedge(beqc))to(aeqc))
13exp14((aeqb)to((beqc)to(aeqc)))