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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
axorbciffatcxorb.2
Assertion
Ref Expression
axorbciffatcxorb

Proof of Theorem axorbciffatcxorb
StepHypRef Expression
1 axorbciffatcxorb.1 . . . . 5
21axorbtnotaiffb 27861 . . . 4
3 xor3 348 . . . 4
42, 3mpbi 201 . . 3
5 axorbciffatcxorb.2 . . 3
64, 5aiffnbandciffatnotciffb 27862 . 2
7 df-xor 1315 . 2
86, 7mpbir 202 1
 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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