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Mirrors > Home > ILE Home > Th. List > pm2.86i | GIF version |
Description: Inference based on pm2.86 94. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 3-Apr-2013.) |
Ref | Expression |
---|---|
pm2.86i.1 | ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜒)) |
Ref | Expression |
---|---|
pm2.86i | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1 5 | . . 3 ⊢ (𝜓 → (𝜑 → 𝜓)) | |
2 | pm2.86i.1 | . . 3 ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜒)) | |
3 | 1, 2 | syl 14 | . 2 ⊢ (𝜓 → (𝜑 → 𝜒)) |
4 | 3 | com12 27 | 1 ⊢ (𝜑 → (𝜓 → 𝜒)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 |
This theorem is referenced by: nfrimi 1418 cbv1 1632 |
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