Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > 2onn | Unicode version |
Description: The ordinal 2 is a natural number. (Contributed by NM, 28-Sep-2004.) |
Ref | Expression |
---|---|
2onn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-2o 6394 | . 2 | |
2 | 1onn 6497 | . . 3 | |
3 | peano2 4577 | . . 3 | |
4 | 2, 3 | ax-mp 5 | . 2 |
5 | 1, 4 | eqeltri 2243 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2141 csuc 4348 com 4572 c1o 6386 c2o 6387 |
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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-13 2143 ax-14 2144 ax-ext 2152 ax-sep 4105 ax-nul 4113 ax-pow 4158 ax-pr 4192 ax-un 4416 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-dif 3123 df-un 3125 df-in 3127 df-ss 3134 df-nul 3415 df-pw 3566 df-sn 3587 df-pr 3588 df-uni 3795 df-int 3830 df-suc 4354 df-iom 4573 df-1o 6393 df-2o 6394 |
This theorem is referenced by: 3onn 6499 nn2m 6503 pw1fin 6885 nninfex 7095 infnninfOLD 7098 nnnninf 7099 isomnimap 7110 enomnilem 7111 fodjuf 7118 ismkvmap 7127 ismkvnex 7128 enmkvlem 7134 iswomnimap 7139 enwomnilem 7142 nninfdcinf 7144 exmidonfinlem 7159 exmidfodomrlemr 7168 exmidfodomrlemrALT 7169 pw1ne3 7196 3nsssucpw1 7202 prarloclemarch2 7370 nq02m 7416 prarloclemlt 7444 prarloclemlo 7445 prarloclem3 7448 prarloclemn 7450 prarloclem5 7451 prarloclemcalc 7453 hash3 10737 unct 12386 2ssom 13799 2o01f 13991 pwle2 13993 pwf1oexmid 13994 subctctexmid 13996 0nninf 13999 nnsf 14000 nninfsellemdc 14005 nninfself 14008 nninffeq 14015 isomninnlem 14024 iswomninnlem 14043 ismkvnnlem 14046 |
Copyright terms: Public domain | W3C validator |