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Mirrors > Home > MPE Home > Th. List > spimev | Structured version Visualization version GIF version |
Description: Distinct-variable version of spime 2392. (Contributed by NM, 10-Jan-1993.) Usage of this theorem is discouraged because it depends on ax-13 2375. Use spimevw 1992 instead. (New usage is discouraged.) |
Ref | Expression |
---|---|
spimev.1 | ⊢ (𝑥 = 𝑦 → (𝜑 → 𝜓)) |
Ref | Expression |
---|---|
spimev | ⊢ (𝜑 → ∃𝑥𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1912 | . 2 ⊢ Ⅎ𝑥𝜑 | |
2 | spimev.1 | . 2 ⊢ (𝑥 = 𝑦 → (𝜑 → 𝜓)) | |
3 | 1, 2 | spime 2392 | 1 ⊢ (𝜑 → ∃𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃wex 1776 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-12 2175 ax-13 2375 |
This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1540 df-ex 1777 df-nf 1781 |
This theorem is referenced by: (None) |
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