Theorem biancomd 271

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 266	. 2 |- ( ( th /\ ch ) <-> ( ch /\ th ) )
3	1, 2	bitrdi 196	1 |- ( ph -> ( ps <-> ( ch /\ th ) ) )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   <-> wb 105

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117

This theorem is used by:  anbi1cd  472  ifpnst  1001  oppr1g  14390  opprunitd  14419  lsslss  14720  znleval  14990  sincosq1sgn  15930  lgsquadlem3  16210  eupth2lem2dc  16712