Theorem aisfbistiaxb

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)

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

Proof

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