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Mirrors > Home > ILE Home > Th. List > mpid | GIF version |
Description: A nested modus ponens deduction. (Contributed by NM, 14-Dec-2004.) |
Ref | Expression |
---|---|
mpid.1 | ⊢ (𝜑 → 𝜒) |
mpid.2 | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
Ref | Expression |
---|---|
mpid | ⊢ (𝜑 → (𝜓 → 𝜃)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpid.1 | . . 3 ⊢ (𝜑 → 𝜒) | |
2 | 1 | a1d 22 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) |
3 | mpid.2 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) | |
4 | 2, 3 | mpdd 36 | 1 ⊢ (𝜑 → (𝜓 → 𝜃)) |
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: mp2d 41 pm2.43a 45 embantd 50 mpan2d 404 ceqsalt 2580 rspcimdv 2657 fvimacnv 5282 riotass2 5494 0mnnnnn0 8214 caucvgre 9580 climcn1 9829 climcn2 9830 |
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