Theorem xoror 1428

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 1426	. 2 ⊢ ((𝜑 ⊻ 𝜓) ↔ ((𝜑 ∨ 𝜓) ∧ (¬ 𝜑 ∨ ¬ 𝜓)))
2	1	simplbi 274	1 ⊢ ((𝜑 ⊻ 𝜓) → (𝜑 ∨ 𝜓))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ∨ wo 720   ⊻ wxo 1424

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 623  ax-in2 624  ax-io 721

This proof depends on definitions:  df-bi 117  df-xor 1425

This theorem is used by:  mtpxor  1475