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Mirrors > Home > MPE Home > Th. List > spimevw | Structured version Visualization version GIF version |
Description: Existential introduction, using implicit substitution. This is to spimew 1976 what spimvw 2000 is to spimw 1975. Version of spimev 2392 and spimefv 2192 with an additional disjoint variable condition, using only Tarski's FOL axiom schemes. (Contributed by NM, 10-Jan-1993.) (Revised by BJ, 17-Mar-2020.) |
Ref | Expression |
---|---|
spimevw.1 | ⊢ (𝑥 = 𝑦 → (𝜑 → 𝜓)) |
Ref | Expression |
---|---|
spimevw | ⊢ (𝜑 → ∃𝑥𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-5 1914 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) | |
2 | spimevw.1 | . 2 ⊢ (𝑥 = 𝑦 → (𝜑 → 𝜓)) | |
3 | 1, 2 | spimew 1976 | 1 ⊢ (𝜑 → ∃𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃wex 1782 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 |
This theorem depends on definitions: df-bi 206 df-ex 1783 |
This theorem is referenced by: dtruALT2 5369 zfpair 5420 exneq 5436 dtruOLD 5442 fvn0ssdmfun 7077 onsupmaxb 41988 refimssco 42358 rlimdmafv 45885 rlimdmafv2 45966 elsprel 46143 |
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