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Mirrors > Home > MPE Home > Th. List > spimev | Structured version Visualization version GIF version |
Description: Distinct-variable version of spime 2244. (Contributed by NM, 10-Jan-1993.) |
Ref | Expression |
---|---|
spimev.1 | ⊢ (𝑥 = 𝑦 → (𝜑 → 𝜓)) |
Ref | Expression |
---|---|
spimev | ⊢ (𝜑 → ∃𝑥𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1830 | . 2 ⊢ Ⅎ𝑥𝜑 | |
2 | spimev.1 | . 2 ⊢ (𝑥 = 𝑦 → (𝜑 → 𝜓)) | |
3 | 1, 2 | spime 2244 | 1 ⊢ (𝜑 → ∃𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃wex 1695 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-12 2034 ax-13 2234 |
This theorem depends on definitions: df-bi 196 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 |
This theorem is referenced by: axsep 4708 dtru 4783 zfpair 4831 fvn0ssdmfun 6258 refimssco 36932 rlimdmafv 39906 |
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