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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 2170 | . . 3 | |
2 | 1 | olci 727 | . 2 |
3 | elsucg 4387 | . 2 | |
4 | 2, 3 | mpbiri 167 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wo 703 wceq 1348 wcel 2141 csuc 4348 |
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 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-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-un 3125 df-sn 3587 df-suc 4354 |
This theorem is referenced by: sucid 4400 nsuceq0g 4401 trsuc 4405 sucssel 4407 ordsucg 4484 sucunielr 4492 suc11g 4539 nlimsucg 4548 peano2b 4597 omsinds 4604 nnpredlt 4606 frecsuclem 6383 phplem4dom 6838 phplem4on 6843 dif1en 6855 fin0 6861 fin0or 6862 fidcenumlemrks 6928 bj-peano4 13955 |
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