![]() |
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 6411 | . 2 ⊢ 1o = suc ∅ | |
2 | 0elon 4389 | . . 3 ⊢ ∅ ∈ On | |
3 | 2 | onsuci 4512 | . 2 ⊢ suc ∅ ∈ On |
4 | 1, 3 | eqeltri 2250 | 1 ⊢ 1o ∈ On |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2148 ∅c0 3422 Oncon0 4360 suc csuc 4362 1oc1o 6404 |
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 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4118 ax-nul 4126 ax-pow 4171 ax-pr 4206 ax-un 4430 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-nul 3423 df-pw 3576 df-sn 3597 df-pr 3598 df-uni 3808 df-tr 4099 df-iord 4363 df-on 4365 df-suc 4368 df-1o 6411 |
This theorem is referenced by: 1oex 6419 2on 6420 2on0 6421 2oconcl 6434 fnoei 6447 oeiexg 6448 oeiv 6451 oei0 6454 oeicl 6457 o1p1e2 6463 oawordriexmid 6465 enpr2d 6811 endisj 6818 snexxph 6943 djuex 7036 1stinr 7069 2ndinr 7070 pm54.43 7183 xpdjuen 7211 prarloclemarch2 7406 bj-el2oss1o 14175 nnsf 14403 |
Copyright terms: Public domain | W3C validator |