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Mirrors > Home > MPE Home > Th. List > vtocle | Structured version Visualization version GIF version |
Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 9-Sep-1993.) Avoid df-clab 2713. (Revised by Wolf Lammen, 31-May-2025.) |
Ref | Expression |
---|---|
vtocle.1 | ⊢ 𝐴 ∈ V |
vtocle.2 | ⊢ (𝑥 = 𝐴 → 𝜑) |
Ref | Expression |
---|---|
vtocle | ⊢ 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vtocle.2 | . 2 ⊢ (𝑥 = 𝐴 → 𝜑) | |
2 | vtocle.1 | . . 3 ⊢ 𝐴 ∈ V | |
3 | 2 | isseti 3496 | . 2 ⊢ ∃𝑥 𝑥 = 𝐴 |
4 | 1, 3 | exlimiiv 1929 | 1 ⊢ 𝜑 |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1537 ∈ wcel 2106 Vcvv 3478 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-8 2108 |
This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1777 df-clel 2814 |
This theorem is referenced by: vtocl 3558 zfrepclf 5297 tz6.12i 6935 eloprabga 7541 eloprabgaOLD 7542 cfflb 10297 axcc3 10476 nn0ind-raph 12716 finxpreclem6 37379 tworepnotupword 46840 |
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