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Mirrors > Home > MPE Home > Th. List > simplim | Structured version Visualization version GIF version |
Description: Simplification. Similar to Theorem *3.26 (Simp) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-1993.) (Proof shortened by Wolf Lammen, 21-Jul-2012.) |
Ref | Expression |
---|---|
simplim | ⊢ (¬ (𝜑 → 𝜓) → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.21 120 | . 2 ⊢ (¬ 𝜑 → (𝜑 → 𝜓)) | |
2 | 1 | con1i 144 | 1 ⊢ (¬ (𝜑 → 𝜓) → 𝜑) |
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: pm2.5 164 pm2.521 166 impt 169 peirce 193 dfbi1 203 biimp 205 imbi12 336 pm4.79 607 mptbi12f 33975 ac6s6 33980 rp-fakeimass 37857 |
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