Mathbox for Jarvin Udandy < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  aistbisfiaxb Structured version   Visualization version   GIF version

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)
 Copyright terms: Public domain W3C validator