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Mirrors > Home > MPE Home > Th. List > simprim | Structured version Visualization version GIF version |
Description: Simplification. Similar to Theorem *3.27 (Simp) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-1993.) (Proof shortened by Wolf Lammen, 13-Nov-2012.) |
Ref | Expression |
---|---|
simprim | ⊢ (¬ (𝜑 → ¬ 𝜓) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | idd 24 | . 2 ⊢ (𝜑 → (𝜓 → 𝜓)) | |
2 | 1 | impi 164 | 1 ⊢ (¬ (𝜑 → ¬ 𝜓) → 𝜓) |
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: impt 178 impbi 207 biimpr 219 imbi12 347 |
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