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Theorem 3orbi123 28594
Description: pm4.39 842 with a 3-conjunct antecedent. This proof is 3orbi123VD 28962 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 957 . 2  |-  ( ( ( ph  <->  ps )  /\  ( ch  <->  th )  /\  ( ta  <->  et )
)  ->  ( ph  <->  ps ) )
2 simp2 958 . 2  |-  ( ( ( ph  <->  ps )  /\  ( ch  <->  th )  /\  ( ta  <->  et )
)  ->  ( ch  <->  th ) )
3 simp3 959 . 2  |-  ( ( ( ph  <->  ps )  /\  ( ch  <->  th )  /\  ( ta  <->  et )
)  ->  ( ta  <->  et ) )
41, 2, 33orbi123d 1253 1  |-  ( ( ( ph  <->  ps )  /\  ( ch  <->  th )  /\  ( ta  <->  et )
)  ->  ( ( ph  \/  ch  \/  ta ) 
<->  ( ps  \/  th  \/  et ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177    \/ w3o 935    /\ w3a 936
This theorem is referenced by:  sbcoreleleq  28619  sbcoreleleqVD  28971
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  df-3an 938
  Copyright terms: Public domain W3C validator