Theorem aistbisfiaxb 43512

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 43490	. 2 ⊢ 𝜑
3		aistbisfiaxb.2	. . 3 ⊢ (𝜓 ↔ ⊥)
4	3	aisfina 43491	. 2 ⊢ ¬ 𝜓
5	2, 4	abnotbtaxb 43508	1 ⊢ (𝜑 ⊻ 𝜓)

Syntax hints:   ↔ wb 209   ⊻ wxo 1502  ⊤wtru 1539  ⊥wfal 1550

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 210  df-an 400  df-xor 1503  df-tru 1541  df-fal 1551

This theorem is referenced by: (None)