Theorem aistbisfiaxb

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)

	Ref	Expression
Hypotheses	aistbisfiaxb.1	⊢ ( 𝜑 ↔ ⊤ )
	aistbisfiaxb.2	⊢ ( 𝜓 ↔ ⊥ )
Assertion	aistbisfiaxb	⊢ ( 𝜑 ⊻ 𝜓 )

Proof

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