![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > 2onOLD | Structured version Visualization version GIF version |
Description: Obsolete version of 2on 8494 as of 30-Nov-2024. (Contributed by NM, 18-Feb-2004.) (Proof shortened by Andrew Salmon, 12-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
2onOLD | ⊢ 2o ∈ On |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-2o 8481 | . 2 ⊢ 2o = suc 1o | |
2 | 1on 8492 | . . 3 ⊢ 1o ∈ On | |
3 | 2 | onsuci 7836 | . 2 ⊢ suc 1o ∈ On |
4 | 1, 3 | eqeltri 2824 | 1 ⊢ 2o ∈ On |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2099 Oncon0 6363 suc csuc 6365 1oc1o 8473 2oc2o 8474 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-ext 2698 ax-sep 5293 ax-nul 5300 ax-pr 5423 ax-un 7734 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 847 df-3or 1086 df-3an 1087 df-tru 1537 df-fal 1547 df-ex 1775 df-sb 2061 df-clab 2705 df-cleq 2719 df-clel 2805 df-ne 2936 df-ral 3057 df-rex 3066 df-rab 3428 df-v 3471 df-dif 3947 df-un 3949 df-in 3951 df-ss 3961 df-pss 3963 df-nul 4319 df-if 4525 df-pw 4600 df-sn 4625 df-pr 4627 df-op 4631 df-uni 4904 df-br 5143 df-opab 5205 df-tr 5260 df-eprel 5576 df-po 5584 df-so 5585 df-fr 5627 df-we 5629 df-ord 6366 df-on 6367 df-suc 6369 df-1o 8480 df-2o 8481 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |