Theorem nbior 887

Description: If two propositions are not equivalent, then at least one is true. (Contributed by BJ, 19-Apr-2019.) (Proof shortened by Wolf Lammen, 19-Jan-2020.)

Assertion

Ref	Expression
nbior	⊢ (¬ (𝜑 ↔ 𝜓) → (𝜑 ∨ 𝜓))

Proof of Theorem nbior

Step	Hyp	Ref	Expression
1		norbi 886	. 2 ⊢ (¬ (𝜑 ∨ 𝜓) → (𝜑 ↔ 𝜓))
2	1	con1i 147	1 ⊢ (¬ (𝜑 ↔ 𝜓) → (𝜑 ∨ 𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 206   ∨ wo 847

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 207  df-or 848

This theorem is referenced by:  nmogtmnf  30790  nmopgtmnf  31888