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Mirrors > Home > MPE Home > Th. List > spimev | Structured version Visualization version GIF version |
Description: Distinct-variable version of spime 2256. (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 1843 | . 2 ⊢ Ⅎ𝑥𝜑 | |
2 | spimev.1 | . 2 ⊢ (𝑥 = 𝑦 → (𝜑 → 𝜓)) | |
3 | 1, 2 | spime 2256 | 1 ⊢ (𝜑 → ∃𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃wex 1704 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-12 2047 ax-13 2246 |
This theorem depends on definitions: df-bi 197 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 |
This theorem is referenced by: axsep 4780 dtru 4857 zfpair 4904 fvn0ssdmfun 6350 refimssco 37913 rlimdmafv 41257 elsprel 41725 |
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