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Mirrors > Home > ILE Home > Th. List > pm2.45 | GIF version |
Description: Theorem *2.45 of [WhiteheadRussell] p. 106. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm2.45 | ⊢ (¬ (𝜑 ∨ 𝜓) → ¬ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orc 633 | . 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓)) | |
2 | 1 | con3i 562 | 1 ⊢ (¬ (𝜑 ∨ 𝜓) → ¬ 𝜑) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∨ wo 629 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-in1 544 ax-in2 545 ax-io 630 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: pm2.47 659 ioran 669 dn1dc 867 eueq3dc 2715 |
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