Theorem biancomd 269

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 264	. 2 |- ( ( th /\ ch ) <-> ( ch /\ th ) )
3	1, 2	bitrdi 195	1 |- ( ph -> ( ps <-> ( ch /\ th ) ) )

Syntax hints:   -> wi 4   /\ 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:  anbi1cd  465  sincosq1sgn  13541