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Theorem axorbciffatcxorb 27863
Description: Given a is equivalent to NOT b, c is equivalent to a. there exists a proof for ( c xor b ) . (Contributed by Jarvin Udandy, 7-Sep-2016.)
Hypotheses
Ref Expression
axorbciffatcxorb.1  |-  ( ph  \/_ 
ps )
axorbciffatcxorb.2  |-  ( ch  <->  ph )
Assertion
Ref Expression
axorbciffatcxorb  |-  ( ch 
\/_  ps )

Proof of Theorem axorbciffatcxorb
StepHypRef Expression
1 axorbciffatcxorb.1 . . . . 5  |-  ( ph  \/_ 
ps )
21axorbtnotaiffb 27861 . . . 4  |-  -.  ( ph 
<->  ps )
3 xor3 348 . . . 4  |-  ( -.  ( ph  <->  ps )  <->  (
ph 
<->  -.  ps ) )
42, 3mpbi 201 . . 3  |-  ( ph  <->  -. 
ps )
5 axorbciffatcxorb.2 . . 3  |-  ( ch  <->  ph )
64, 5aiffnbandciffatnotciffb 27862 . 2  |-  -.  ( ch 
<->  ps )
7 df-xor 1315 . 2  |-  ( ( ch  \/_  ps )  <->  -.  ( ch  <->  ps )
)
86, 7mpbir 202 1  |-  ( ch 
\/_  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 178    \/_ wxo 1314
This theorem is referenced by:  mdandyvrx0  27916  mdandyvrx1  27917  mdandyvrx2  27918  mdandyvrx3  27919  mdandyvrx4  27920  mdandyvrx5  27921  mdandyvrx6  27922  mdandyvrx7  27923
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 179  df-xor 1315
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