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Theorem axorbtnotaiffb 40833
Description: Given a is exclusive to b, there exists a proof for (not (a if-and-only-if b)); df-xor 1463 is a closed form of this. (Contributed by Jarvin Udandy, 7-Sep-2016.)
Hypothesis
Ref Expression
axorbtnotaiffb.1 (𝜑𝜓)
Assertion
Ref Expression
axorbtnotaiffb ¬ (𝜑𝜓)

Proof of Theorem axorbtnotaiffb
StepHypRef Expression
1 axorbtnotaiffb.1 . 2 (𝜑𝜓)
2 df-xor 1463 . 2 ((𝜑𝜓) ↔ ¬ (𝜑𝜓))
31, 2mpbi 220 1 ¬ (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196  wxo 1462
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  df-xor 1463
This theorem is referenced by:  axorbciffatcxorb  40835  aifftbifffaibifff  40852
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