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Theorem 3orbi123 32360
Description: pm4.39 869 with a 3-conjunct antecedent. This proof is 3orbi123VD 32730 automatically translated and minimized. (Contributed by Alan Sare, 31-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
3orbi123  |-  ( ( ( ph  <->  ps )  /\  ( ch  <->  th )  /\  ( ta  <->  et )
)  ->  ( ( ph  \/  ch  \/  ta ) 
<->  ( ps  \/  th  \/  et ) ) )

Proof of Theorem 3orbi123
StepHypRef Expression
1 simp1 996 . 2  |-  ( ( ( ph  <->  ps )  /\  ( ch  <->  th )  /\  ( ta  <->  et )
)  ->  ( ph  <->  ps ) )
2 simp2 997 . 2  |-  ( ( ( ph  <->  ps )  /\  ( ch  <->  th )  /\  ( ta  <->  et )
)  ->  ( ch  <->  th ) )
3 simp3 998 . 2  |-  ( ( ( ph  <->  ps )  /\  ( ch  <->  th )  /\  ( ta  <->  et )
)  ->  ( ta  <->  et ) )
41, 2, 33orbi123d 1298 1  |-  ( ( ( ph  <->  ps )  /\  ( ch  <->  th )  /\  ( ta  <->  et )
)  ->  ( ( ph  \/  ch  \/  ta ) 
<->  ( ps  \/  th  \/  et ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184    \/ w3o 972    /\ w3a 973
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 185  df-or 370  df-an 371  df-3or 974  df-3an 975
This theorem is referenced by:  sbcoreleleq  32385  sbcoreleleqVD  32739
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