Theorem anbi12ci 679

Description: Variant of anbi12i 678 with commutation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)

Hypotheses

Ref	Expression
anbi12.1	|- (ph <-> ps)
anbi12.2	|- (ch <-> th)

Assertion

Ref	Expression
anbi12ci	|- ((ph /\ ch) <-> (th /\ ps))

Proof of Theorem anbi12ci

Step	Hyp	Ref	Expression
1		anbi12.1	. . 3 |- (ph <-> ps)
2		anbi12.2	. . 3 |- (ch <-> th)
3	1, 2	anbi12i 678	. 2 |- ((ph /\ ch) <-> (ps /\ th))
4		ancom 437	. 2 |- ((ps /\ th) <-> (th /\ ps))
5	3, 4	bitri 240	1 |- ((ph /\ ch) <-> (th /\ ps))

Syntax hints:   <-> wb 176   /\ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  funsex  5829  refex  5912  foundex  5915  csucex  6260