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Theorem ifpan123g 35801
Description: Conjunction of conditional logical operators. (Contributed by RP, 18-Apr-2020.)
Assertion
Ref Expression
ifpan123g  |-  ( (if- ( ph ,  ch ,  ta )  /\ if- ( ps ,  th ,  et ) )  <->  ( (
( -.  ph  \/  ch )  /\  ( ph  \/  ta ) )  /\  ( ( -. 
ps  \/  th )  /\  ( ps  \/  et ) ) ) )

Proof of Theorem ifpan123g
StepHypRef Expression
1 dfifp4 1424 . 2  |-  (if- (
ph ,  ch ,  ta )  <->  ( ( -. 
ph  \/  ch )  /\  ( ph  \/  ta ) ) )
2 dfifp4 1424 . 2  |-  (if- ( ps ,  th ,  et )  <->  ( ( -. 
ps  \/  th )  /\  ( ps  \/  et ) ) )
31, 2anbi12i 701 1  |-  ( (if- ( ph ,  ch ,  ta )  /\ if- ( ps ,  th ,  et ) )  <->  ( (
( -.  ph  \/  ch )  /\  ( ph  \/  ta ) )  /\  ( ( -. 
ps  \/  th )  /\  ( ps  \/  et ) ) ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 187    \/ wo 369    /\ wa 370  if-wif 1420
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 188  df-or 371  df-an 372  df-ifp 1421
This theorem is referenced by:  ifpan23  35802
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