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Metamath Proof Explorer

Theorem mpbiran2

Description: Detach truth from conjunction in biconditional. (Contributed by NM, 22-Feb-1996)

Ref Expression
Hypotheses mpbiran2.1 
|- ch
mpbiran2.2 
|- ( ph <-> ( ps /\ ch ) )
Assertion mpbiran2 
|- ( ph <-> ps )

Proof

Step Hyp Ref Expression
1 mpbiran2.1 
 |-  ch
2 mpbiran2.2 
 |-  ( ph <-> ( ps /\ ch ) )
3 2 biancomi 
 |-  ( ph <-> ( ch /\ ps ) )
4 1 3 mpbiran 
 |-  ( ph <-> ps )