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Metamath Proof Explorer

Theorem biancomd

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

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

Proof

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