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Mirrors > Home > ILE Home > Th. List > onirri | Unicode version |
Description: An ordinal number is not a member of itself. Theorem 7M(c) of [Enderton] p. 192. (Contributed by NM, 11-Jun-1994.) |
Ref | Expression |
---|---|
onirri.1 |
Ref | Expression |
---|---|
onirri |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | onirri.1 | . . 3 | |
2 | 1 | onordi 4399 | . 2 |
3 | ordirr 4514 | . 2 | |
4 | 2, 3 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wcel 2135 word 4335 con0 4336 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 ax-setind 4509 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ne 2335 df-ral 2447 df-rex 2448 df-v 2724 df-dif 3114 df-in 3118 df-ss 3125 df-sn 3577 df-uni 3785 df-tr 4076 df-iord 4339 df-on 4341 |
This theorem is referenced by: ontri2orexmidim 4544 enpr2d 6775 pm54.43 7138 pw1ne1 7177 |
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