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Mirrors > Home > MPE Home > Th. List > vtocldOLD | Structured version Visualization version GIF version |
Description: Obsolete version of vtocld 3509 as of 2-Sep-2024. (Contributed by Mario Carneiro, 15-Oct-2016.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
vtocld.1 | ⊢ (𝜑 → 𝐴 ∈ 𝑉) |
vtocld.2 | ⊢ ((𝜑 ∧ 𝑥 = 𝐴) → (𝜓 ↔ 𝜒)) |
vtocld.3 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
vtocldOLD | ⊢ (𝜑 → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vtocld.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ 𝑉) | |
2 | vtocld.2 | . 2 ⊢ ((𝜑 ∧ 𝑥 = 𝐴) → (𝜓 ↔ 𝜒)) | |
3 | vtocld.3 | . 2 ⊢ (𝜑 → 𝜓) | |
4 | nfv 1917 | . 2 ⊢ Ⅎ𝑥𝜑 | |
5 | nfcvd 2906 | . 2 ⊢ (𝜑 → Ⅎ𝑥𝐴) | |
6 | nfvd 1918 | . 2 ⊢ (𝜑 → Ⅎ𝑥𝜒) | |
7 | 1, 2, 3, 4, 5, 6 | vtocldf 3508 | 1 ⊢ (𝜑 → 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 205 ∧ wa 396 = wceq 1541 ∈ wcel 2106 |
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 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-10 2137 ax-11 2154 ax-12 2171 ax-ext 2707 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 846 df-3an 1089 df-ex 1782 df-nf 1786 df-cleq 2728 df-clel 2814 df-nfc 2887 |
This theorem is referenced by: (None) |
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