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Theorem aistbisfiaxb 41600
Description: Given a is equivalent to T., Given b is equivalent to F. there exists a proof for a-xor-b. (Contributed by Jarvin Udandy, 31-Aug-2016.)
Hypotheses
Ref Expression
aistbisfiaxb.1 (𝜑 ↔ ⊤)
aistbisfiaxb.2 (𝜓 ↔ ⊥)
Assertion
Ref Expression
aistbisfiaxb (𝜑𝜓)

Proof of Theorem aistbisfiaxb
StepHypRef Expression
1 aistbisfiaxb.1 . . 3 (𝜑 ↔ ⊤)
21aistia 41578 . 2 𝜑
3 aistbisfiaxb.2 . . 3 (𝜓 ↔ ⊥)
43aisfina 41579 . 2 ¬ 𝜓
52, 4abnotbtaxb 41596 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wb 196  wxo 1611  wtru 1631  wfal 1635
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-an 383  df-xor 1612  df-tru 1633  df-fal 1636
This theorem is referenced by: (None)
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