Theorem xoror 1369

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 1367	. 2 ⊢ ((𝜑 ⊻ 𝜓) ↔ ((𝜑 ∨ 𝜓) ∧ (¬ 𝜑 ∨ ¬ 𝜓)))
2	1	simplbi 272	1 ⊢ ((𝜑 ⊻ 𝜓) → (𝜑 ∨ 𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 698   ⊻ wxo 1365

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699

This theorem depends on definitions:  df-bi 116  df-xor 1366

This theorem is referenced by:  mtpxor  1416