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Theorem anbi1 461
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 19 . 2  |-  ( (
ph 
<->  ps )  ->  ( ph 
<->  ps ) )
21anbi1d 460 1  |-  ( (
ph 
<->  ps )  ->  (
( ph  /\  ch )  <->  ( ps  /\  ch )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  pm5.75  946  expap0  10347  rexfiuz  10785
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