Mathbox for BJ |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-vtoclg1f | Structured version Visualization version GIF version |
Description: Reprove vtoclg1f 3564 from bj-vtoclg1f1 34130. This removes dependency on ax-ext 2790, df-cleq 2811 and df-v 3494. Use bj-vtoclg1fv 34132 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 | bj-elisset 34089 | . 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 34125 | . 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 1528 ∃wex 1771 Ⅎwnf 1775 ∈ wcel 2105 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-12 2167 |
This theorem depends on definitions: df-bi 208 df-an 397 df-ex 1772 df-nf 1776 df-sb 2061 df-clab 2797 df-clel 2890 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |