Theorem notbicom 43860

Description: Commutative law for the negation of a biconditional. (Contributed by Glauco Siliprandi, 15-Feb-2025.)

Hypothesis

Ref	Expression
notbicom.1	⊢ ¬ (𝜑 ↔ 𝜓)

Assertion

Ref	Expression
notbicom	⊢ ¬ (𝜓 ↔ 𝜑)

Proof of Theorem notbicom

Step	Hyp	Ref	Expression
1		notbicom.1	. 2 ⊢ ¬ (𝜑 ↔ 𝜓)
2		bicom 221	. 2 ⊢ ((𝜓 ↔ 𝜑) ↔ (𝜑 ↔ 𝜓))
3	1, 2	mtbir 323	1 ⊢ ¬ (𝜓 ↔ 𝜑)

Syntax hints:  ¬ wn 3   ↔ wb 205

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 206

This theorem is referenced by: (None)