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Theorem xoror 1286
Description: XOR implies OR. (Contributed by BJ, 19-Apr-2019.)
Assertion
Ref Expression
xoror ((𝜑𝜓) → (𝜑𝜓))

Proof of Theorem xoror
StepHypRef Expression
1 xoranor 1284 . 2 ((𝜑𝜓) ↔ ((𝜑𝜓) ∧ (¬ 𝜑 ∨ ¬ 𝜓)))
21simplbi 263 1 ((𝜑𝜓) → (𝜑𝜓))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wo 639  wxo 1282
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-io 640
This theorem depends on definitions:  df-bi 114  df-xor 1283
This theorem is referenced by:  mtpxor  1333
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