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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-vtocl | Structured version Visualization version GIF version |
Description: Remove dependency on ax-ext 2795, df-clab 2802 and df-cleq 2816 (and df-sb 2070 and df-v 3498) from vtocl 3561. (Contributed by BJ, 6-Oct-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-vtocl.s | ⊢ 𝐴 ∈ 𝑉 |
bj-vtocl.maj | ⊢ (𝑥 = 𝐴 → (𝜑 ↔ 𝜓)) |
bj-vtocl.min | ⊢ 𝜑 |
Ref | Expression |
---|---|
bj-vtocl | ⊢ 𝜓 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1915 | . 2 ⊢ Ⅎ𝑥𝜓 | |
2 | bj-vtocl.s | . 2 ⊢ 𝐴 ∈ 𝑉 | |
3 | bj-vtocl.maj | . 2 ⊢ (𝑥 = 𝐴 → (𝜑 ↔ 𝜓)) | |
4 | bj-vtocl.min | . 2 ⊢ 𝜑 | |
5 | 1, 2, 3, 4 | bj-vtoclf 34233 | 1 ⊢ 𝜓 |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 208 = wceq 1537 ∈ wcel 2114 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-12 2177 |
This theorem depends on definitions: df-bi 209 df-an 399 df-ex 1781 df-nf 1785 df-clel 2895 |
This theorem is referenced by: (None) |
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