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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-omssonALT | GIF version |
Description: Alternate proof of bj-omsson 13957. (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 13956 | . 2 ⊢ ω ∈ On | |
2 | onss 4475 | . 2 ⊢ (ω ∈ On → ω ⊆ On) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ω ⊆ On |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2141 ⊆ wss 3121 Oncon0 4346 ωcom 4572 |
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-in1 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-13 2143 ax-14 2144 ax-ext 2152 ax-nul 4113 ax-pr 4192 ax-un 4416 ax-bd0 13808 ax-bdor 13811 ax-bdal 13813 ax-bdex 13814 ax-bdeq 13815 ax-bdel 13816 ax-bdsb 13817 ax-bdsep 13879 ax-infvn 13936 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-rab 2457 df-v 2732 df-dif 3123 df-un 3125 df-in 3127 df-ss 3134 df-nul 3415 df-sn 3587 df-pr 3588 df-uni 3795 df-int 3830 df-tr 4086 df-iord 4349 df-on 4351 df-suc 4354 df-iom 4573 df-bdc 13836 df-bj-ind 13922 |
This theorem is referenced by: (None) |
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