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Theorem xorbi12i 1378
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 1377 . 2  |-  ( T. 
->  ( ( ph  \/_  ch ) 
<->  ( ps  \/_  th )
) )
65mptru 1357 1  |-  ( (
ph  \/_  ch )  <->  ( ps  \/_  th )
)
Colors of variables: wff set class
Syntax hints:    <-> wb 104   T. wtru 1349    \/_ wxo 1370
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 609  ax-in2 610  ax-io 704
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-xor 1371
This theorem is referenced by: (None)
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