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Mirrors > Home > MPE Home > Th. List > pm2.5g | Structured version Visualization version GIF version |
Description: General instance of Theorem *2.5 of [WhiteheadRussell] p. 107. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 9-Oct-2012.) |
Ref | Expression |
---|---|
pm2.5g | ⊢ (¬ (𝜑 → 𝜓) → (¬ 𝜑 → 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simplim 170 | . 2 ⊢ (¬ (𝜑 → 𝜓) → 𝜑) | |
2 | 1 | pm2.24d 154 | 1 ⊢ (¬ (𝜑 → 𝜓) → (¬ 𝜑 → 𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem is referenced by: pm2.5 172 pm5.11g 943 |
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