Theorem biancomd 33995

Description: Commuting conjunction in a biconditional, deduction form. (Contributed by Peter Mazsa, 3-Oct-2018.)

Hypothesis

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

Assertion

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

Proof of Theorem biancomd

Step	Hyp	Ref	Expression
1		biancomd.1	. 2 |- ( ph -> ( ps <-> ( th /\ ch ) ) )
2		ancom 466	. 2 |- ( ( th /\ ch ) <-> ( ch /\ th ) )
3	1, 2	syl6bb 276	1 |- ( ph -> ( ps <-> ( ch /\ th ) ) )

Syntax hints:   -> wi 4   <-> 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:  anbi1cd  33997