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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-sucex | GIF version |
Description: sucex 4191 from bounded separation. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-sucex.1 | ⊢ A ∈ V |
Ref | Expression |
---|---|
bj-sucex | ⊢ suc A ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-sucex.1 | . 2 ⊢ A ∈ V | |
2 | bj-sucexg 9377 | . 2 ⊢ (A ∈ V → suc A ∈ V) | |
3 | 1, 2 | ax-mp 7 | 1 ⊢ suc A ∈ V |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1390 Vcvv 2551 suc csuc 4068 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-13 1401 ax-14 1402 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 ax-pr 3935 ax-un 4136 ax-bd0 9268 ax-bdor 9271 ax-bdex 9274 ax-bdeq 9275 ax-bdel 9276 ax-bdsb 9277 ax-bdsep 9339 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-rex 2306 df-v 2553 df-un 2916 df-sn 3373 df-pr 3374 df-uni 3572 df-suc 4074 df-bdc 9296 |
This theorem is referenced by: bj-indint 9390 bj-bdfindis 9407 bj-inf2vnlem1 9430 |
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