Theorem bilani 387

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

Hypothesis

Ref	Expression
birani.1	|- ( ph <-> ps )

Assertion

Ref	Expression
bilani	|- ( ( ch /\ ph ) -> ps )

Proof of Theorem bilani

Step	Hyp	Ref	Expression
1		birani.1	. . 3 |- ( ph <-> ps )
2	1	biimpi 120	. 2 |- ( ph -> ps )
3	2	adantl 277	1 |- ( ( ch /\ ph ) -> ps )

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:  f1setfi  7317