![]() |
Mathbox for BJ |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > Mathboxes > elab2a | GIF version |
Description: One implication of elab 2896. (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 1539 | . 2 ⊢ Ⅎ𝑥𝜓 | |
2 | elab2a.s | . 2 ⊢ 𝐴 ∈ V | |
3 | elab2a.1 | . 2 ⊢ (𝑥 = 𝐴 → (𝜓 → 𝜑)) | |
4 | 1, 2, 3 | elabf2 14972 | 1 ⊢ (𝜓 → 𝐴 ∈ {𝑥 ∣ 𝜑}) |
Colors of variables: wff set class |
Syntax hints: → wi 4 = wceq 1364 ∈ wcel 2160 {cab 2175 Vcvv 2752 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-v 2754 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |