Theorem aisfbistiaxb 43150

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	⊢ (𝜑 ⊻ 𝜓)

Proof of Theorem aisfbistiaxb

Step	Hyp	Ref	Expression
1		aisfbistiaxb.1	. . 3 ⊢ (𝜑 ↔ ⊥)
2	1	aisfina 43128	. 2 ⊢ ¬ 𝜑
3		aisfbistiaxb.2	. . 3 ⊢ (𝜓 ↔ ⊤)
4	3	aistia 43127	. 2 ⊢ 𝜓
5	2, 4	abnotataxb 43146	1 ⊢ (𝜑 ⊻ 𝜓)

Syntax hints:   ↔ wb 208   ⊻ wxo 1500  ⊤wtru 1534  ⊥wfal 1545

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 209  df-an 399  df-or 844  df-xor 1501  df-tru 1536  df-fal 1546

This theorem is referenced by: (None)