Metamath Proof Explorer

Theorem bilani

Description: Inference adding a conjunct to the left-hand side of a biconditional. (Contributed by Matthew House, 22-May-2026)

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

Proof

Step Hyp Ref Expression
1 birani.1 
 |-  ( ph <-> ps )
2 1 biimpi 
 |-  ( ph -> ps )
3 2 adantl 
 |-  ( ( ch /\ ph ) -> ps )