This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem anbi2

Description: Introduce a left conjunct to both sides of a logical equivalence. (Contributed by NM, 16-Nov-2013)

Ref Expression
Assertion anbi2 
|- ( ( ph <-> ps ) -> ( ( ch /\ ph ) <-> ( ch /\ ps ) ) )

Proof

Step Hyp Ref Expression
1 id 
 |-  ( ( ph <-> ps ) -> ( ph <-> ps ) )
2 1 anbi2d 
 |-  ( ( ph <-> ps ) -> ( ( ch /\ ph ) <-> ( ch /\ ps ) ) )