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Mirrors > Home > ILE Home > Th. List > vtocle | GIF version |
Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 9-Sep-1993.) |
Ref | Expression |
---|---|
vtocle.1 | ⊢ 𝐴 ∈ V |
vtocle.2 | ⊢ (𝑥 = 𝐴 → 𝜑) |
Ref | Expression |
---|---|
vtocle | ⊢ 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vtocle.1 | . 2 ⊢ 𝐴 ∈ V | |
2 | vtocle.2 | . . 3 ⊢ (𝑥 = 𝐴 → 𝜑) | |
3 | 2 | vtocleg 2801 | . 2 ⊢ (𝐴 ∈ V → 𝜑) |
4 | 1, 3 | ax-mp 5 | 1 ⊢ 𝜑 |
Colors of variables: wff set class |
Syntax hints: → wi 4 = wceq 1348 ∈ wcel 2141 Vcvv 2730 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1440 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-v 2732 |
This theorem is referenced by: repizf2 4146 nn0ind-raph 9322 |
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