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 ) ) )