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Mirrors > Home > ILE Home > Th. List > sucidg | Unicode version |
Description: Part of Proposition 7.23 of [TakeutiZaring] p. 41 (generalized). (Contributed by NM, 25-Mar-1995.) (Proof shortened by Scott Fenton, 20-Feb-2012.) |
Ref | Expression |
---|---|
sucidg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2164 | . . 3 | |
2 | 1 | olci 722 | . 2 |
3 | elsucg 4376 | . 2 | |
4 | 2, 3 | mpbiri 167 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wo 698 wceq 1342 wcel 2135 csuc 4337 |
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-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 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 df-un 3115 df-sn 3576 df-suc 4343 |
This theorem is referenced by: sucid 4389 nsuceq0g 4390 trsuc 4394 sucssel 4396 ordsucg 4473 sucunielr 4481 suc11g 4528 nlimsucg 4537 peano2b 4586 omsinds 4593 nnpredlt 4595 frecsuclem 6365 phplem4dom 6819 phplem4on 6824 dif1en 6836 fin0 6842 fin0or 6843 fidcenumlemrks 6909 bj-peano4 13678 |
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