Theorem biancom 33994

Description: Commuting conjunction in a biconditional. (Contributed by Peter Mazsa, 17-Jun-2018.)

Hypothesis

Ref	Expression
biancom.1	|- ( ph <-> ( ch /\ ps ) )

Assertion

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

Proof of Theorem biancom

Step	Hyp	Ref	Expression
1		biancom.1	. 2 |- ( ph <-> ( ch /\ ps ) )
2		ancom 466	. 2 |- ( ( ps /\ ch ) <-> ( ch /\ ps ) )
3	1, 2	bitr4i 267	1 |- ( ph <-> ( ps /\ ch ) )

Syntax hints:   <-> wb 196   /\ wa 384

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 197  df-an 386

This theorem is referenced by:  anbi1ci  33996  rabeqel  34019  iss2  34112