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Theorem anbi1 690
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 21 . 2  |-  ( (
ph 
<->  ps )  ->  ( ph 
<->  ps ) )
21anbi1d 688 1  |-  ( (
ph 
<->  ps )  ->  (
( ph  /\  ch )  <->  ( ps  /\  ch )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178    /\ wa 360
This theorem is referenced by:  pm5.75  908  rexfiuz  11708  relexpindlem  23207  nabi1  24002  bnj916  27751
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-an 362
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