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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-omssonALT | GIF version |
Description: Alternate proof of bj-omsson 15378. (Contributed by BJ, 27-Oct-2020.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bj-omssonALT | ⊢ ω ⊆ On |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-omelon 15377 | . 2 ⊢ ω ∈ On | |
2 | onss 4517 | . 2 ⊢ (ω ∈ On → ω ⊆ On) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ω ⊆ On |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2160 ⊆ wss 3149 Oncon0 4388 ωcom 4614 |
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-in1 615 ax-in2 616 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-nul 4151 ax-pr 4234 ax-un 4458 ax-bd0 15229 ax-bdor 15232 ax-bdal 15234 ax-bdex 15235 ax-bdeq 15236 ax-bdel 15237 ax-bdsb 15238 ax-bdsep 15300 ax-infvn 15357 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-rab 2477 df-v 2758 df-dif 3151 df-un 3153 df-in 3155 df-ss 3162 df-nul 3443 df-sn 3620 df-pr 3621 df-uni 3832 df-int 3867 df-tr 4124 df-iord 4391 df-on 4393 df-suc 4396 df-iom 4615 df-bdc 15257 df-bj-ind 15343 |
This theorem is referenced by: (None) |
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