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| Mirrors > Home > MPE Home > Th. List > vtocleOLD | Structured version Visualization version GIF version | ||
| Description: Obsolete version of vtocle 3555 as of 31-May-2025. (Contributed by NM, 9-Sep-1993.) (Proof modification is discouraged.) (New usage is discouraged.) | 
| Ref | Expression | 
|---|---|
| vtocle.1 | ⊢ 𝐴 ∈ V | 
| vtocle.2 | ⊢ (𝑥 = 𝐴 → 𝜑) | 
| Ref | Expression | 
|---|---|
| vtocleOLD | ⊢ 𝜑 | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | vtocle.1 | . 2 ⊢ 𝐴 ∈ V | |
| 2 | vtocle.2 | . . 3 ⊢ (𝑥 = 𝐴 → 𝜑) | |
| 3 | 2 | vtocleg 3553 | . 2 ⊢ (𝐴 ∈ V → 𝜑) | 
| 4 | 1, 3 | ax-mp 5 | 1 ⊢ 𝜑 | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 = wceq 1540 ∈ wcel 2108 Vcvv 3480 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1543 df-ex 1780 df-sb 2065 df-clab 2715 df-clel 2816 | 
| This theorem is referenced by: (None) | 
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