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Theorem axorbciffatcxorb 37891
 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 37889 . . . 4
3 xor3 358 . . . 4
42, 3mpbi 211 . . 3
5 axorbciffatcxorb.2 . . 3
64, 5aiffnbandciffatnotciffb 37890 . 2
7 df-xor 1401 . 2
86, 7mpbir 212 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wb 187   wxo 1400 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 188  df-xor 1401 This theorem is referenced by:  mdandyvrx0  37959  mdandyvrx1  37960  mdandyvrx2  37961  mdandyvrx3  37962  mdandyvrx4  37963  mdandyvrx5  37964  mdandyvrx6  37965  mdandyvrx7  37966
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