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Mirrors > Home > ILE Home > Th. List > Mathboxes > elab2a | GIF version |
Description: One implication of elab 2802. (Contributed by BJ, 21-Nov-2019.) |
Ref | Expression |
---|---|
elab2a.s | ⊢ 𝐴 ∈ V |
elab2a.1 | ⊢ (𝑥 = 𝐴 → (𝜓 → 𝜑)) |
Ref | Expression |
---|---|
elab2a | ⊢ (𝜓 → 𝐴 ∈ {𝑥 ∣ 𝜑}) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1493 | . 2 ⊢ Ⅎ𝑥𝜓 | |
2 | elab2a.s | . 2 ⊢ 𝐴 ∈ V | |
3 | elab2a.1 | . 2 ⊢ (𝑥 = 𝐴 → (𝜓 → 𝜑)) | |
4 | 1, 2, 3 | elabf2 12916 | 1 ⊢ (𝜓 → 𝐴 ∈ {𝑥 ∣ 𝜑}) |
Colors of variables: wff set class |
Syntax hints: → wi 4 = wceq 1316 ∈ wcel 1465 {cab 2103 Vcvv 2660 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 |
This theorem is referenced by: (None) |
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