Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 2139 | . . 3 | |
2 | 1 | olci 721 | . 2 |
3 | elsucg 4326 | . 2 | |
4 | 2, 3 | mpbiri 167 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wo 697 wceq 1331 wcel 1480 csuc 4287 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-un 3075 df-sn 3533 df-suc 4293 |
This theorem is referenced by: sucid 4339 nsuceq0g 4340 trsuc 4344 sucssel 4346 ordsucg 4418 sucunielr 4426 suc11g 4472 nlimsucg 4481 peano2b 4528 omsinds 4535 frecsuclem 6303 phplem4dom 6756 phplem4on 6761 dif1en 6773 fin0 6779 fin0or 6780 fidcenumlemrks 6841 bj-peano4 13153 |
Copyright terms: Public domain | W3C validator |