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Theorem anbi2 688
Description: Introduce a left conjunct to both sides of a logical equivalence. (Contributed by NM, 16-Nov-2013.)
Assertion
Ref Expression
anbi2  |-  ( (
ph 
<->  ps )  ->  (
( ch  /\  ph ) 
<->  ( ch  /\  ps ) ) )

Proof of Theorem anbi2
StepHypRef Expression
1 id 19 . 2  |-  ( (
ph 
<->  ps )  ->  ( ph 
<->  ps ) )
21anbi2d 684 1  |-  ( (
ph 
<->  ps )  ->  (
( ch  /\  ph ) 
<->  ( ch  /\  ps ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358
This theorem is referenced by:  nabi2  24829
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
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