Theorem aisbnaxb

Description: Given a is equivalent to b, there exists a proof for (not (a xor b)). (Contributed by Jarvin Udandy, 28-Aug-2016)

	Ref	Expression
Hypothesis	aisbnaxb.1	⊢ ( 𝜑 ↔ 𝜓 )
Assertion	aisbnaxb	⊢ ¬ ( 𝜑 ⊻ 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		aisbnaxb.1	⊢ ( 𝜑 ↔ 𝜓 )
2	1	notnoti	⊢ ¬ ¬ ( 𝜑 ↔ 𝜓 )
3		df-xor	⊢ ( ( 𝜑 ⊻ 𝜓 ) ↔ ¬ ( 𝜑 ↔ 𝜓 ) )
4	2 3	mtbir	⊢ ¬ ( 𝜑 ⊻ 𝜓 )