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Mirrors > Home > MPE Home > Th. List > 2onOLD | Structured version Visualization version GIF version |
Description: Obsolete version of 2on 8427 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 8414 | . 2 ⊢ 2o = suc 1o | |
2 | 1on 8425 | . . 3 ⊢ 1o ∈ On | |
3 | 2 | onsuci 7775 | . 2 ⊢ suc 1o ∈ On |
4 | 1, 3 | eqeltri 2834 | 1 ⊢ 2o ∈ On |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2107 Oncon0 6318 suc csuc 6320 1oc1o 8406 2oc2o 8407 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-ext 2708 ax-sep 5257 ax-nul 5264 ax-pr 5385 ax-un 7673 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-3or 1089 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-sb 2069 df-clab 2715 df-cleq 2729 df-clel 2815 df-ne 2945 df-ral 3066 df-rex 3075 df-rab 3409 df-v 3448 df-dif 3914 df-un 3916 df-in 3918 df-ss 3928 df-pss 3930 df-nul 4284 df-if 4488 df-pw 4563 df-sn 4588 df-pr 4590 df-op 4594 df-uni 4867 df-br 5107 df-opab 5169 df-tr 5224 df-eprel 5538 df-po 5546 df-so 5547 df-fr 5589 df-we 5591 df-ord 6321 df-on 6322 df-suc 6324 df-1o 8413 df-2o 8414 |
This theorem is referenced by: (None) |
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