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Mirrors > Home > MPE Home > Th. List > pm2.46 | Structured version Visualization version GIF version |
Description: Theorem *2.46 of [WhiteheadRussell] p. 106. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm2.46 | ⊢ (¬ (𝜑 ∨ 𝜓) → ¬ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | olc 868 | . 2 ⊢ (𝜓 → (𝜑 ∨ 𝜓)) | |
2 | 1 | con3i 154 | 1 ⊢ (¬ (𝜑 ∨ 𝜓) → ¬ 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∨ wo 847 |
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 207 df-or 848 |
This theorem is referenced by: pm2.48 884 pm2.49 885 rb-ax3 1750 eueq3 3719 soasym 5628 ltnsym 11356 tglineneq 28666 expgt0b 32822 unbdqndv2lem1 36491 oexpreposd 42335 nnfoctbdjlem 46410 |
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