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Mirrors > Home > NFE Home > Th. List > mpdi | GIF version |
Description: A nested modus ponens deduction. (Contributed by NM, 16-Apr-2005.) (Proof shortened by O'Cat, 15-Jan-2008.) |
Ref | Expression |
---|---|
mpdi.1 | ⊢ (ψ → χ) |
mpdi.2 | ⊢ (φ → (ψ → (χ → θ))) |
Ref | Expression |
---|---|
mpdi | ⊢ (φ → (ψ → θ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpdi.1 | . . 3 ⊢ (ψ → χ) | |
2 | 1 | a1i 10 | . 2 ⊢ (φ → (ψ → χ)) |
3 | mpdi.2 | . 2 ⊢ (φ → (ψ → (χ → θ))) | |
4 | 2, 3 | mpdd 36 | 1 ⊢ (φ → (ψ → θ)) |
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: mpii 39 pm2.43d 44 impt 149 enpw1 6062 |
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