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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2193 |
. . 3
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2 | 1 | olci 733 |
. 2
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3 | elsucg 4435 |
. 2
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4 | 2, 3 | mpbiri 168 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2175 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2180 df-cleq 2186 df-clel 2189 df-nfc 2325 df-v 2762 df-un 3157 df-sn 3624 df-suc 4402 |
This theorem is referenced by: sucid 4448 nsuceq0g 4449 trsuc 4453 sucssel 4455 ordsucg 4534 sucunielr 4542 suc11g 4589 nlimsucg 4598 peano2b 4647 omsinds 4654 nnpredlt 4656 frecsuclem 6459 phplem4dom 6918 phplem4on 6923 dif1en 6935 fin0 6941 fin0or 6942 fidcenumlemrks 7012 bj-peano4 15447 |
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