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Mirrors > Home > MPE Home > Th. List > jarr | Structured version Visualization version GIF version |
Description: Elimination of a nested antecedent. Sometimes called "Syll-Simp" since it is a syllogism applied to ax-1 6 ("Simplification"). (Contributed by Wolf Lammen, 9-May-2013.) |
Ref | Expression |
---|---|
jarr | ⊢ (((𝜑 → 𝜓) → 𝜒) → (𝜓 → 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1 6 | . 2 ⊢ (𝜓 → (𝜑 → 𝜓)) | |
2 | 1 | imim1i 63 | 1 ⊢ (((𝜑 → 𝜓) → 𝜒) → (𝜓 → 𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 |
This theorem is referenced by: loolin 111 loowoz 112 minimp 1627 bj-stabpeirce 34713 bj-sbievw2 35009 ax3h 44339 adh-jarrsc 44446 adh-minimp 44459 |
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