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Mirrors > Home > ILE Home > Th. List > mpan | GIF version |
Description: An inference based on modus ponens. (Contributed by NM, 30-Aug-1993.) (Proof shortened by Wolf Lammen, 7-Apr-2013.) |
Ref | Expression |
---|---|
mpan.1 | ⊢ φ |
mpan.2 | ⊢ ((φ ∧ ψ) → χ) |
Ref | Expression |
---|---|
mpan | ⊢ (ψ → χ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpan.1 | . . 3 ⊢ φ | |
2 | 1 | a1i 9 | . 2 ⊢ (ψ → φ) |
3 | mpan.2 | . 2 ⊢ ((φ ∧ ψ) → χ) | |
4 | 2, 3 | mpancom 399 | 1 ⊢ (ψ → χ) |
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