Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > 1on | GIF version |
Description: Ordinal 1 is an ordinal number. (Contributed by NM, 29-Oct-1995.) |
Ref | Expression |
---|---|
1on | ⊢ 1o ∈ On |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-1o 6364 | . 2 ⊢ 1o = suc ∅ | |
2 | 0elon 4353 | . . 3 ⊢ ∅ ∈ On | |
3 | 2 | onsuci 4476 | . 2 ⊢ suc ∅ ∈ On |
4 | 1, 3 | eqeltri 2230 | 1 ⊢ 1o ∈ On |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2128 ∅c0 3394 Oncon0 4324 suc csuc 4326 1oc1o 6357 |
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 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-13 2130 ax-14 2131 ax-ext 2139 ax-sep 4083 ax-nul 4091 ax-pow 4136 ax-pr 4170 ax-un 4394 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-nul 3395 df-pw 3545 df-sn 3566 df-pr 3567 df-uni 3774 df-tr 4064 df-iord 4327 df-on 4329 df-suc 4332 df-1o 6364 |
This theorem is referenced by: 1oex 6372 2on 6373 2on0 6374 2oconcl 6387 fnoei 6400 oeiexg 6401 oeiv 6404 oei0 6407 oeicl 6410 o1p1e2 6416 oawordriexmid 6418 enpr2d 6763 endisj 6770 snexxph 6895 djuex 6988 1stinr 7021 2ndinr 7022 pm54.43 7126 xpdjuen 7154 prarloclemarch2 7340 bj-el2oss1o 13390 nnsf 13619 |
Copyright terms: Public domain | W3C validator |