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Mirrors > Home > NFE Home > Th. List > pm2.43d | GIF version |
Description: Deduction absorbing redundant antecedent. (Contributed by NM, 18-Aug-1993.) (Proof shortened by O'Cat, 28-Nov-2008.) |
Ref | Expression |
---|---|
pm2.43d.1 | ⊢ (φ → (ψ → (ψ → χ))) |
Ref | Expression |
---|---|
pm2.43d | ⊢ (φ → (ψ → χ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 | . 2 ⊢ (ψ → ψ) | |
2 | pm2.43d.1 | . 2 ⊢ (φ → (ψ → (ψ → χ))) | |
3 | 1, 2 | mpdi 38 | 1 ⊢ (φ → (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: loolinALT 95 ax12 1935 ax10lem4 1941 ax12from12o 2156 rgen2a 2680 rspct 2948 ncfinraise 4481 funssres 5144 2elresin 5194 |
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