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Theorem anbi1 688
Description: Introduce a right conjunct to both sides of a logical equivalence. Theorem *4.36 of [WhiteheadRussell] p. 118. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
anbi1  |-  ( (
ph 
<->  ps )  ->  (
( ph  /\  ch )  <->  ( ps  /\  ch )
) )

Proof of Theorem anbi1
StepHypRef Expression
1 id 20 . 2  |-  ( (
ph 
<->  ps )  ->  ( ph 
<->  ps ) )
21anbi1d 686 1  |-  ( (
ph 
<->  ps )  ->  (
( ph  /\  ch )  <->  ( ps  /\  ch )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177    /\ wa 359
This theorem is referenced by:  pm5.75  904  nanbi1  1304  rexfiuz  12139  relexpindlem  25127  bnj916  29158
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 178  df-an 361
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