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Mirrors > Home > ILE Home > Th. List > tfr1onlem3ag | Unicode version |
Description: Lemma for transfinite recursion. This lemma changes some bound variables in (version of tfrlem3ag 6256 but for tfr1on 6297 related lemmas). (Contributed by Jim Kingdon, 13-Mar-2022.) |
Ref | Expression |
---|---|
tfr1onlem3ag.1 |
Ref | Expression |
---|---|
tfr1onlem3ag |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fneq12 5263 | . . . 4 | |
2 | simpll 519 | . . . . . . 7 | |
3 | simpr 109 | . . . . . . 7 | |
4 | 2, 3 | fveq12d 5475 | . . . . . 6 |
5 | 2, 3 | reseq12d 4867 | . . . . . . 7 |
6 | 5 | fveq2d 5472 | . . . . . 6 |
7 | 4, 6 | eqeq12d 2172 | . . . . 5 |
8 | simplr 520 | . . . . 5 | |
9 | 7, 8 | cbvraldva2 2687 | . . . 4 |
10 | 1, 9 | anbi12d 465 | . . 3 |
11 | 10 | cbvrexdva 2690 | . 2 |
12 | tfr1onlem3ag.1 | . 2 | |
13 | 11, 12 | elab2g 2859 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1335 wcel 2128 cab 2143 wral 2435 wrex 2436 cres 4588 wfn 5165 cfv 5170 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3773 df-br 3966 df-opab 4026 df-xp 4592 df-rel 4593 df-cnv 4594 df-co 4595 df-dm 4596 df-res 4598 df-iota 5135 df-fun 5172 df-fn 5173 df-fv 5178 |
This theorem is referenced by: tfr1onlem3 6285 tfr1onlemsucaccv 6288 tfr1onlembxssdm 6290 tfr1onlemres 6296 |
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