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Theorem xorbi12i 1319
Description: Equality property for XOR. (Contributed by Mario Carneiro, 4-Sep-2016.)
Hypotheses
Ref Expression
xorbi12.1  |-  ( ph  <->  ps )
xorbi12.2  |-  ( ch  <->  th )
Assertion
Ref Expression
xorbi12i  |-  ( (
ph  \/_  ch )  <->  ( ps  \/_  th )
)

Proof of Theorem xorbi12i
StepHypRef Expression
1 xorbi12.1 . . . 4  |-  ( ph  <->  ps )
21a1i 9 . . 3  |-  ( T. 
->  ( ph  <->  ps )
)
3 xorbi12.2 . . . 4  |-  ( ch  <->  th )
43a1i 9 . . 3  |-  ( T. 
->  ( ch  <->  th )
)
52, 4xorbi12d 1318 . 2  |-  ( T. 
->  ( ( ph  \/_  ch ) 
<->  ( ps  \/_  th )
) )
65mptru 1298 1  |-  ( (
ph  \/_  ch )  <->  ( ps  \/_  th )
)
Colors of variables: wff set class
Syntax hints:    <-> wb 103   T. wtru 1290    \/_ wxo 1311
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-io 665
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-xor 1312
This theorem is referenced by: (None)
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