Theorem xoror 1515

Description: Exclusive disjunction implies disjunction ("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		xor2 1514	. 2 ⊢ ((𝜑 ⊻ 𝜓) ↔ ((𝜑 ∨ 𝜓) ∧ ¬ (𝜑 ∧ 𝜓)))
2	1	simplbi 501	1 ⊢ ((𝜑 ⊻ 𝜓) → (𝜑 ∨ 𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 399   ∨ wo 847   ⊻ wxo 1507

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 210  df-an 400  df-or 848  df-xor 1508

This theorem is referenced by:  mtpxor  1779  afv2orxorb  44580