Theorem xoror 1270

Description: XOR implies OR. (Contributed by BJ, 19-Apr-2019.)

Assertion

Ref	Expression
xoror	⊢ ((𝜑 ⊻ 𝜓) → (𝜑 ∨ 𝜓))

Proof of Theorem xoror

Step	Hyp	Ref	Expression
1		xoranor 1268	. 2 ⊢ ((𝜑 ⊻ 𝜓) ↔ ((𝜑 ∨ 𝜓) ∧ (¬ 𝜑 ∨ ¬ 𝜓)))
2	1	simplbi 259	1 ⊢ ((𝜑 ⊻ 𝜓) → (𝜑 ∨ 𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 629   ⊻ wxo 1266

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630

This theorem depends on definitions:  df-bi 110  df-xor 1267

This theorem is referenced by:  mtpxor  1317