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Mirrors > Home > ILE Home > Th. List > spimv | GIF version |
Description: A version of spim 1626 with a distinct variable requirement instead of a bound variable hypothesis. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
spimv.1 | ⊢ (𝑥 = 𝑦 → (𝜑 → 𝜓)) |
Ref | Expression |
---|---|
spimv | ⊢ (∀𝑥𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1421 | . 2 ⊢ Ⅎ𝑥𝜓 | |
2 | spimv.1 | . 2 ⊢ (𝑥 = 𝑦 → (𝜑 → 𝜓)) | |
3 | 1, 2 | spim 1626 | 1 ⊢ (∀𝑥𝜑 → 𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∀wal 1241 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 df-nf 1350 |
This theorem is referenced by: aev 1693 ax16i 1738 spv 1740 reu6 2730 el 3931 |
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