Theorem biancomi 268

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

Hypothesis

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

Assertion

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

Proof of Theorem biancomi

Step	Hyp	Ref	Expression
1		biancomi.1	. 2 |- ( ph <-> ( ch /\ ps ) )
2		ancom 264	. 2 |- ( ( ps /\ ch ) <-> ( ch /\ ps ) )
3	1, 2	bitr4i 186	1 |- ( ph <-> ( ps /\ ch ) )

Syntax hints:   /\ wa 103   <-> wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)