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Mirrors > Home > MPE Home > Th. List > xoror | Structured version Visualization version GIF version |
Description: XOR implies OR. (Contributed by BJ, 19-Apr-2019.) |
Ref | Expression |
---|---|
xoror | ⊢ ((𝜑 ⊻ 𝜓) → (𝜑 ∨ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xor2 1645 | . 2 ⊢ ((𝜑 ⊻ 𝜓) ↔ ((𝜑 ∨ 𝜓) ∧ ¬ (𝜑 ∧ 𝜓))) | |
2 | 1 | simplbi 493 | 1 ⊢ ((𝜑 ⊻ 𝜓) → (𝜑 ∨ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∧ wa 386 ∨ wo 880 ⊻ wxo 1639 |
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 199 df-an 387 df-or 881 df-xor 1640 |
This theorem is referenced by: mtpxor 1872 afv2orxorb 42130 |
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