Theorem aisbnaxb 43141

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

Hypothesis

Ref	Expression
aisbnaxb.1	⊢ (𝜑 ↔ 𝜓)

Assertion

Ref	Expression
aisbnaxb	⊢ ¬ (𝜑 ⊻ 𝜓)

Proof of Theorem aisbnaxb

Step	Hyp	Ref	Expression
1		aisbnaxb.1	. . 3 ⊢ (𝜑 ↔ 𝜓)
2	1	notnoti 145	. 2 ⊢ ¬ ¬ (𝜑 ↔ 𝜓)
3		df-xor 1501	. 2 ⊢ ((𝜑 ⊻ 𝜓) ↔ ¬ (𝜑 ↔ 𝜓))
4	2, 3	mtbir 325	1 ⊢ ¬ (𝜑 ⊻ 𝜓)

Syntax hints:  ¬ wn 3   ↔ wb 208   ⊻ wxo 1500

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-xor 1501

This theorem is referenced by:  dandysum2p2e4  43228