Metamath Proof Explorer


Theorem anbi2i

Description: Introduce a left conjunct to both sides of a logical equivalence. (Contributed by NM, 3-Jan-1993) (Proof shortened by Wolf Lammen, 16-Nov-2013)

Ref Expression
Hypothesis anbi.1
|- ( ph <-> ps )
Assertion anbi2i
|- ( ( ch /\ ph ) <-> ( ch /\ ps ) )

Proof

Step Hyp Ref Expression
1 anbi.1
 |-  ( ph <-> ps )
2 1 a1i
 |-  ( ch -> ( ph <-> ps ) )
3 2 pm5.32i
 |-  ( ( ch /\ ph ) <-> ( ch /\ ps ) )