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Theorem anbi1 712
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 23 . 2  |-  ( (
ph 
<->  ps )  ->  ( ph 
<->  ps ) )
21anbi1d 710 1  |-  ( (
ph 
<->  ps )  ->  (
( ph  /\  ch )  <->  ( ps  /\  ch )
) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 188    /\ wa 371
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 189  df-an 373
This theorem is referenced by:  pm5.75  946  nanbi1  1392  relexpindlem  13120  rexfiuz  13404  bnj916  29746
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