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Mirrors > Home > MPE Home > Th. List > anmp | Structured version Visualization version GIF version |
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 850 | . 2 ⊢ (𝜑 → 𝜓) |
4 | 1, 3 | ax-mp 5 | 1 ⊢ 𝜓 |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∨ wo 842 |
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 208 df-or 843 |
This theorem is referenced by: rbsyl 1742 rblem1 1743 rblem2 1744 rblem4 1746 rblem5 1747 rblem6 1748 rblem7 1749 re1axmp 1750 re2luk1 1751 re2luk2 1752 re2luk3 1753 |
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