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Mirrors > Home > MPE Home > Th. List > spi | Structured version Visualization version GIF version |
Description: Inference rule of universal instantiation, or universal specialization. Converse of the inference rule of (universal) generalization ax-gen 1787. Contrary to the rule of generalization, its closed form is valid, see sp 2172. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
spi.1 | ⊢ ∀𝑥𝜑 |
Ref | Expression |
---|---|
spi | ⊢ 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | spi.1 | . 2 ⊢ ∀𝑥𝜑 | |
2 | sp 2172 | . 2 ⊢ (∀𝑥𝜑 → 𝜑) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ 𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ∀wal 1526 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-12 2167 |
This theorem depends on definitions: df-bi 208 df-ex 1772 |
This theorem is referenced by: dariiALT 2746 barbariALT 2750 festinoALT 2755 barocoALT 2757 daraptiALT 2765 kmlem2 9565 axac2 9876 axac 9877 axaci 9878 bnj864 32093 rr-grothprim 40513 |
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