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Theorem aiffnbandciffatnotciffb 40362
Description: Given a is equivalent to (not b), c is equivalent to a, there exists a proof for ( not ( c iff b ) ). (Contributed by Jarvin Udandy, 7-Sep-2016.)
Hypotheses
Ref Expression
aiffnbandciffatnotciffb.1 (𝜑 ↔ ¬ 𝜓)
aiffnbandciffatnotciffb.2 (𝜒𝜑)
Assertion
Ref Expression
aiffnbandciffatnotciffb ¬ (𝜒𝜓)

Proof of Theorem aiffnbandciffatnotciffb
StepHypRef Expression
1 aiffnbandciffatnotciffb.2 . . 3 (𝜒𝜑)
2 aiffnbandciffatnotciffb.1 . . 3 (𝜑 ↔ ¬ 𝜓)
31, 2bitri 264 . 2 (𝜒 ↔ ¬ 𝜓)
4 xor3 372 . 2 (¬ (𝜒𝜓) ↔ (𝜒 ↔ ¬ 𝜓))
53, 4mpbir 221 1 ¬ (𝜒𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196
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 197
This theorem is referenced by:  axorbciffatcxorb  40363
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