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Mirrors > Home > ILE Home > Th. List > spimev | GIF version |
Description: Distinct-variable version of spime 1669. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
spimev.1 | ⊢ (𝑥 = 𝑦 → (𝜑 → 𝜓)) |
Ref | Expression |
---|---|
spimev | ⊢ (𝜑 → ∃𝑥𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1461 | . 2 ⊢ Ⅎ𝑥𝜑 | |
2 | spimev.1 | . 2 ⊢ (𝑥 = 𝑦 → (𝜑 → 𝜓)) | |
3 | 1, 2 | spime 1669 | 1 ⊢ (𝜑 → ∃𝑥𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∃wex 1421 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 |
This theorem is referenced by: speiv 1783 rnxpid 4775 |
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