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Mirrors > Home > MPE Home > Th. List > vtoclgOLD | Structured version Visualization version GIF version |
Description: Obsolete version of vtoclg 3515 as of 20-Apr-2024. (Contributed by NM, 17-Apr-1995.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
vtoclgOLD.1 | ⊢ (𝑥 = 𝐴 → (𝜑 ↔ 𝜓)) |
vtoclgOLD.2 | ⊢ 𝜑 |
Ref | Expression |
---|---|
vtoclgOLD | ⊢ (𝐴 ∈ 𝑉 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1915 | . 2 ⊢ Ⅎ𝑥𝜓 | |
2 | vtoclgOLD.1 | . 2 ⊢ (𝑥 = 𝐴 → (𝜑 ↔ 𝜓)) | |
3 | vtoclgOLD.2 | . 2 ⊢ 𝜑 | |
4 | 1, 2, 3 | vtoclg1f 3514 | 1 ⊢ (𝐴 ∈ 𝑉 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 209 = wceq 1538 ∈ wcel 2111 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2113 ax-9 2121 ax-12 2175 ax-ext 2770 |
This theorem depends on definitions: df-bi 210 df-an 400 df-ex 1782 df-nf 1786 df-cleq 2791 df-clel 2870 |
This theorem is referenced by: (None) |
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