Theorem xoror 1379

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 1377	. 2 ⊢ ((𝜑 ⊻ 𝜓) ↔ ((𝜑 ∨ 𝜓) ∧ (¬ 𝜑 ∨ ¬ 𝜓)))
2	1	simplbi 274	1 ⊢ ((𝜑 ⊻ 𝜓) → (𝜑 ∨ 𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 708   ⊻ wxo 1375

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-io 709

This theorem depends on definitions:  df-bi 117  df-xor 1376

This theorem is referenced by:  mtpxor  1426