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Theorem xorbi12i 1323
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 )
2 xorbi12.2 . . . 4  |-  ( ch  <->  th )
31, 2bibi12i 307 . . 3  |-  ( (
ph 
<->  ch )  <->  ( ps  <->  th ) )
43notbii 288 . 2  |-  ( -.  ( ph  <->  ch )  <->  -.  ( ps  <->  th )
)
5 df-xor 1314 . 2  |-  ( (
ph  \/_  ch )  <->  -.  ( ph  <->  ch )
)
6 df-xor 1314 . 2  |-  ( ( ps  \/_  th )  <->  -.  ( ps  <->  th )
)
74, 5, 63bitr4i 269 1  |-  ( (
ph  \/_  ch )  <->  ( ps  \/_  th )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 177    \/_ wxo 1313
This theorem is referenced by:  hadcoma  1397  hadcomb  1398  hadnot  1402
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-xor 1314
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