Theorem aistbisfiaxb 39735

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	⊢ (𝜑 ⊻ 𝜓)

Proof of Theorem aistbisfiaxb

Step	Hyp	Ref	Expression
1		aistbisfiaxb.1	. . 3 ⊢ (𝜑 ↔ ⊤)
2	1	aistia 39713	. 2 ⊢ 𝜑
3		aistbisfiaxb.2	. . 3 ⊢ (𝜓 ↔ ⊥)
4	3	aisfina 39714	. 2 ⊢ ¬ 𝜓
5	2, 4	abnotbtaxb 39731	1 ⊢ (𝜑 ⊻ 𝜓)

Syntax hints:   ↔ wb 195   ⊻ wxo 1456  ⊤wtru 1476  ⊥wfal 1480

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 196  df-an 385  df-xor 1457  df-tru 1478  df-fal 1481

This theorem is referenced by: (None)