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Mirrors > Home > ILE Home > Th. List > sucinc | Unicode version |
Description: Successor is increasing. (Contributed by Jim Kingdon, 25-Jun-2019.) |
Ref | Expression |
---|---|
sucinc.1 |
Ref | Expression |
---|---|
sucinc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sssucid 4398 | . . 3 | |
2 | vex 2733 | . . . 4 | |
3 | 2 | sucex 4481 | . . . 4 |
4 | suceq 4385 | . . . . 5 | |
5 | sucinc.1 | . . . . 5 | |
6 | 4, 5 | fvmptg 5570 | . . . 4 |
7 | 2, 3, 6 | mp2an 424 | . . 3 |
8 | 1, 7 | sseqtrri 3182 | . 2 |
9 | 8 | ax-gen 1442 | 1 |
Colors of variables: wff set class |
Syntax hints: wal 1346 wceq 1348 wcel 2141 cvv 2730 wss 3121 cmpt 4048 csuc 4348 cfv 5196 |
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-13 2143 ax-14 2144 ax-ext 2152 ax-sep 4105 ax-pow 4158 ax-pr 4192 ax-un 4416 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-sbc 2956 df-un 3125 df-in 3127 df-ss 3134 df-pw 3566 df-sn 3587 df-pr 3588 df-op 3590 df-uni 3795 df-br 3988 df-opab 4049 df-mpt 4050 df-id 4276 df-suc 4354 df-xp 4615 df-rel 4616 df-cnv 4617 df-co 4618 df-dm 4619 df-iota 5158 df-fun 5198 df-fv 5204 |
This theorem is referenced by: (None) |
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