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Theorem xoror 1514
Description: Exclusive disjunction implies disjunction ("XOR implies OR"). (Contributed by BJ, 19-Apr-2019.)
Assertion
Ref Expression
xoror ((𝜑𝜓) → (𝜑𝜓))

Proof of Theorem xoror
StepHypRef Expression
1 xor2 1513 . 2 ((𝜑𝜓) ↔ ((𝜑𝜓) ∧ ¬ (𝜑𝜓)))
21simplbi 501 1 ((𝜑𝜓) → (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wa 399  wo 846  wxo 1506
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 847  df-xor 1507
This theorem is referenced by:  mtpxor  1778  afv2orxorb  44253
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