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Mirrors > Home > MPE Home > Th. List > xoror | Structured version Visualization version GIF version |
Description: Exclusive disjunction implies disjunction ("XOR implies OR"). (Contributed by BJ, 19-Apr-2019.) |
Ref | Expression |
---|---|
xoror | ⊢ ((𝜑 ⊻ 𝜓) → (𝜑 ∨ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xor2 1513 | . 2 ⊢ ((𝜑 ⊻ 𝜓) ↔ ((𝜑 ∨ 𝜓) ∧ ¬ (𝜑 ∧ 𝜓))) | |
2 | 1 | simplbi 501 | 1 ⊢ ((𝜑 ⊻ 𝜓) → (𝜑 ∨ 𝜓)) |
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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