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| Description: Modus ponens for { ∨ , ¬ } axiom systems. (Contributed by Anthony Hart, 12-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.) | 
| Ref | Expression | 
|---|---|
| anmp.min | ⊢ 𝜑 | 
| anmp.maj | ⊢ (¬ 𝜑 ∨ 𝜓) | 
| Ref | Expression | 
|---|---|
| anmp | ⊢ 𝜓 | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | anmp.min | . 2 ⊢ 𝜑 | |
| 2 | anmp.maj | . . 3 ⊢ (¬ 𝜑 ∨ 𝜓) | |
| 3 | 2 | imorri 855 | . 2 ⊢ (𝜑 → 𝜓) | 
| 4 | 1, 3 | ax-mp 5 | 1 ⊢ 𝜓 | 
| Colors of variables: wff setvar class | 
| Syntax hints: ¬ wn 3 ∨ wo 847 | 
| 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 207 df-or 848 | 
| This theorem is referenced by: rbsyl 1755 rblem1 1756 rblem2 1757 rblem4 1759 rblem5 1760 rblem6 1761 rblem7 1762 re1axmp 1763 re2luk1 1764 re2luk2 1765 re2luk3 1766 | 
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