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Theorem aisfbistiaxb 41601
 Description: Given a is equivalent to F., Given b is equivalent to T., there exists a proof for a-xor-b. (Contributed by Jarvin Udandy, 31-Aug-2016.)
Hypotheses
Ref Expression
aisfbistiaxb.1 (𝜑 ↔ ⊥)
aisfbistiaxb.2 (𝜓 ↔ ⊤)
Assertion
Ref Expression
aisfbistiaxb (𝜑𝜓)

Proof of Theorem aisfbistiaxb
StepHypRef Expression
1 aisfbistiaxb.1 . . 3 (𝜑 ↔ ⊥)
21aisfina 41579 . 2 ¬ 𝜑
3 aisfbistiaxb.2 . . 3 (𝜓 ↔ ⊤)
43aistia 41578 . 2 𝜓
52, 4abnotataxb 41597 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-or 827  df-xor 1612  df-tru 1633  df-fal 1636 This theorem is referenced by: (None)
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