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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-omsson | GIF version |
Description: Constructive proof of omsson 4641. See also bj-omssonALT 15393. (Contributed by BJ, 27-Oct-2020.) (Proof modification is discouraged.) (New usage is discouraged. |
Ref | Expression |
---|---|
bj-omsson | ⊢ ω ⊆ On |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-nnelon 15389 | . 2 ⊢ (𝑥 ∈ ω → 𝑥 ∈ On) | |
2 | 1 | ssriv 3183 | 1 ⊢ ω ⊆ On |
Colors of variables: wff set class |
Syntax hints: ⊆ wss 3153 Oncon0 4392 ωcom 4618 |
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 2166 ax-14 2167 ax-ext 2175 ax-nul 4155 ax-pr 4238 ax-un 4462 ax-bd0 15243 ax-bdor 15246 ax-bdal 15248 ax-bdex 15249 ax-bdeq 15250 ax-bdel 15251 ax-bdsb 15252 ax-bdsep 15314 ax-infvn 15371 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2180 df-cleq 2186 df-clel 2189 df-nfc 2325 df-ral 2477 df-rex 2478 df-rab 2481 df-v 2762 df-dif 3155 df-un 3157 df-in 3159 df-ss 3166 df-nul 3447 df-sn 3624 df-pr 3625 df-uni 3836 df-int 3871 df-tr 4128 df-iord 4395 df-on 4397 df-suc 4400 df-iom 4619 df-bdc 15271 df-bj-ind 15357 |
This theorem is referenced by: (None) |
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