Theorem aisfbistiaxb 47989

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 47967	. 2 ⊢ ¬ 𝜑
3		aisfbistiaxb.2	. . 3 ⊢ (𝜓 ↔ ⊤)
4	3	aistia 47966	. 2 ⊢ 𝜓
5	2, 4	abnotataxb 47985	1 ⊢ (𝜑 ⊻ 𝜓)

This proof depends on syntax axioms:   ↔ wb 209   ⊻ wxo 1541  ⊤wtru 1571  ⊥wfal 1582

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-xor 1542  df-tru 1573  df-fal 1583

This theorem is used by: (None)