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Mirrors > Home > NFE Home > Th. List > pm2.61ian | GIF version |
Description: Elimination of an antecedent. (Contributed by NM, 1-Jan-2005.) |
Ref | Expression |
---|---|
pm2.61ian.1 | ⊢ ((φ ∧ ψ) → χ) |
pm2.61ian.2 | ⊢ ((¬ φ ∧ ψ) → χ) |
Ref | Expression |
---|---|
pm2.61ian | ⊢ (ψ → χ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.61ian.1 | . . 3 ⊢ ((φ ∧ ψ) → χ) | |
2 | 1 | ex 423 | . 2 ⊢ (φ → (ψ → χ)) |
3 | pm2.61ian.2 | . . 3 ⊢ ((¬ φ ∧ ψ) → χ) | |
4 | 3 | ex 423 | . 2 ⊢ (¬ φ → (ψ → χ)) |
5 | 2, 4 | pm2.61i 156 | 1 ⊢ (ψ → χ) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∧ wa 358 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 177 df-an 360 |
This theorem is referenced by: 4cases 915 consensus 925 sbcom 2089 ax11indalem 2197 phi11lem1 4595 xpcan2 5058 |
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