Theorem anbi12ci 434

Description: Variant of anbi12i 433 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 433	. 2 |- ( ( ph /\ ch ) <-> ( ps /\ th ) )
4		ancom 253	. 2 |- ( ( ps /\ th ) <-> ( th /\ ps ) )
5	3, 4	bitri 173	1 |- ( ( ph /\ ch ) <-> ( th /\ ps ) )

Syntax hints:   /\ wa 97   <-> wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  opelopabsbALT  3996  cnvpom  4860  f1cnvcnv  5100