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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-vtoclg1f | Structured version Visualization version GIF version |
Description: Reprove vtoclg1f 3569 from bj-vtoclg1f1 36860. This removes dependency on ax-ext 2704, df-cleq 2725 and df-v 3479. Use bj-vtoclg1fv 36862 instead when sufficient (in particular when 𝑉 is substituted for V). (Contributed by BJ, 14-Sep-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-vtoclg1f.nf | ⊢ Ⅎ𝑥𝜓 |
bj-vtoclg1f.maj | ⊢ (𝑥 = 𝐴 → (𝜑 → 𝜓)) |
bj-vtoclg1f.min | ⊢ 𝜑 |
Ref | Expression |
---|---|
bj-vtoclg1f | ⊢ (𝐴 ∈ 𝑉 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2819 | . 2 ⊢ (𝐴 ∈ 𝑉 → ∃𝑥 𝑥 = 𝐴) | |
2 | bj-vtoclg1f.nf | . . 3 ⊢ Ⅎ𝑥𝜓 | |
3 | bj-vtoclg1f.maj | . . 3 ⊢ (𝑥 = 𝐴 → (𝜑 → 𝜓)) | |
4 | bj-vtoclg1f.min | . . 3 ⊢ 𝜑 | |
5 | 2, 3, 4 | bj-exlimmpi 36855 | . 2 ⊢ (∃𝑥 𝑥 = 𝐴 → 𝜓) |
6 | 1, 5 | syl 17 | 1 ⊢ (𝐴 ∈ 𝑉 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1535 ∃wex 1774 Ⅎwnf 1778 ∈ wcel 2104 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1963 ax-7 2003 ax-8 2106 ax-12 2173 |
This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1538 df-ex 1775 df-nf 1779 df-sb 2061 df-clab 2711 df-clel 2812 |
This theorem is referenced by: (None) |
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