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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-ceqsalv | Structured version Visualization version GIF version |
Description: Remove from ceqsalv 3532 dependency on ax-ext 2793 (and on df-cleq 2814, df-v 3496, df-clab 2800, df-sb 2070). (Contributed by BJ, 12-Oct-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-ceqsalv.1 | ⊢ 𝐴 ∈ V |
bj-ceqsalv.2 | ⊢ (𝑥 = 𝐴 → (𝜑 ↔ 𝜓)) |
Ref | Expression |
---|---|
bj-ceqsalv | ⊢ (∀𝑥(𝑥 = 𝐴 → 𝜑) ↔ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1915 | . 2 ⊢ Ⅎ𝑥𝜓 | |
2 | bj-ceqsalv.1 | . 2 ⊢ 𝐴 ∈ V | |
3 | bj-ceqsalv.2 | . 2 ⊢ (𝑥 = 𝐴 → (𝜑 ↔ 𝜓)) | |
4 | 1, 2, 3 | bj-ceqsal 34212 | 1 ⊢ (∀𝑥(𝑥 = 𝐴 → 𝜑) ↔ 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 208 ∀wal 1535 = wceq 1537 ∈ wcel 2114 Vcvv 3494 |
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-3an 1085 df-ex 1781 df-nf 1785 df-clel 2893 |
This theorem is referenced by: (None) |
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