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Theorem xorbi12d 1360
Description: Deduction joining two equivalences to form equivalence of exclusive-or. (Contributed by Jim Kingdon, 7-Oct-2018.)
Hypotheses
Ref Expression
xorbi12d.1  |-  ( ph  ->  ( ps  <->  ch )
)
xorbi12d.2  |-  ( ph  ->  ( th  <->  ta )
)
Assertion
Ref Expression
xorbi12d  |-  ( ph  ->  ( ( ps  \/_  th )  <->  ( ch  \/_  ta ) ) )

Proof of Theorem xorbi12d
StepHypRef Expression
1 xorbi12d.1 . . 3  |-  ( ph  ->  ( ps  <->  ch )
)
21xorbi1d 1359 . 2  |-  ( ph  ->  ( ( ps  \/_  th )  <->  ( ch  \/_  th ) ) )
3 xorbi12d.2 . . 3  |-  ( ph  ->  ( th  <->  ta )
)
43xorbi2d 1358 . 2  |-  ( ph  ->  ( ( ch  \/_  th )  <->  ( ch  \/_  ta ) ) )
52, 4bitrd 187 1  |-  ( ph  ->  ( ( ps  \/_  th )  <->  ( ch  \/_  ta ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104    \/_ wxo 1353
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698
This theorem depends on definitions:  df-bi 116  df-xor 1354
This theorem is referenced by:  xorbi12i  1361  anxordi  1378  rpnegap  9481
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