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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-sucex | GIF version |
Description: sucex 4523 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 15338 | . 2 ⊢ (𝐴 ∈ V → suc 𝐴 ∈ V) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ suc 𝐴 ∈ V |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2160 Vcvv 2756 suc csuc 4390 |
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-13 2162 ax-14 2163 ax-ext 2171 ax-pr 4234 ax-un 4458 ax-bd0 15229 ax-bdor 15232 ax-bdex 15235 ax-bdeq 15236 ax-bdel 15237 ax-bdsb 15238 ax-bdsep 15300 |
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-rex 2474 df-v 2758 df-un 3153 df-sn 3620 df-pr 3621 df-uni 3832 df-suc 4396 df-bdc 15257 |
This theorem is referenced by: bj-indint 15347 bj-bdfindis 15363 bj-inf2vnlem1 15386 |
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