Theorem anbi2ci 459

Description: Variant of anbi2i 457 with commutation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)

Hypothesis

Ref	Expression
bi.aa	|- ( ph <-> ps )

Assertion

Ref	Expression
anbi2ci	|- ( ( ph /\ ch ) <-> ( ch /\ ps ) )

Proof of Theorem anbi2ci

Step	Hyp	Ref	Expression
1		bi.aa	. . 3 |- ( ph <-> ps )
2	1	anbi1i 458	. 2 |- ( ( ph /\ ch ) <-> ( ps /\ ch ) )
3		ancom 266	. 2 |- ( ( ps /\ ch ) <-> ( ch /\ ps ) )
4	2, 3	bitri 184	1 |- ( ( ph /\ ch ) <-> ( ch /\ ps ) )

Syntax hints:   /\ wa 104   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  clabel  2304  ordpwsucss  4565  asymref  5013  supmoti  6989  eqger  13014  xmeter  13807