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Mirrors > Home > ILE Home > Th. List > caucvgprprlemcbv | Unicode version |
Description: Lemma for caucvgprpr 7488. Change bound variables in Cauchy condition. (Contributed by Jim Kingdon, 12-Feb-2021.) |
Ref | Expression |
---|---|
caucvgprpr.f | |
caucvgprpr.cau |
Ref | Expression |
---|---|
caucvgprprlemcbv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caucvgprpr.cau | . 2 | |
2 | breq1 3902 | . . . 4 | |
3 | fveq2 5389 | . . . . . 6 | |
4 | opeq1 3675 | . . . . . . . . . . . 12 | |
5 | 4 | eceq1d 6433 | . . . . . . . . . . 11 |
6 | 5 | fveq2d 5393 | . . . . . . . . . 10 |
7 | 6 | breq2d 3911 | . . . . . . . . 9 |
8 | 7 | abbidv 2235 | . . . . . . . 8 |
9 | 6 | breq1d 3909 | . . . . . . . . 9 |
10 | 9 | abbidv 2235 | . . . . . . . 8 |
11 | 8, 10 | opeq12d 3683 | . . . . . . 7 |
12 | 11 | oveq2d 5758 | . . . . . 6 |
13 | 3, 12 | breq12d 3912 | . . . . 5 |
14 | 3, 11 | oveq12d 5760 | . . . . . 6 |
15 | 14 | breq2d 3911 | . . . . 5 |
16 | 13, 15 | anbi12d 464 | . . . 4 |
17 | 2, 16 | imbi12d 233 | . . 3 |
18 | breq2 3903 | . . . 4 | |
19 | fveq2 5389 | . . . . . . 7 | |
20 | 19 | oveq1d 5757 | . . . . . 6 |
21 | 20 | breq2d 3911 | . . . . 5 |
22 | 19 | breq1d 3909 | . . . . 5 |
23 | 21, 22 | anbi12d 464 | . . . 4 |
24 | 18, 23 | imbi12d 233 | . . 3 |
25 | 17, 24 | cbvral2v 2639 | . 2 |
26 | 1, 25 | sylib 121 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 cab 2103 wral 2393 cop 3500 class class class wbr 3899 wf 5089 cfv 5093 (class class class)co 5742 c1o 6274 cec 6395 cnpi 7048 clti 7051 ceq 7055 crq 7060 cltq 7061 cnp 7067 cpp 7069 cltp 7071 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-xp 4515 df-cnv 4517 df-dm 4519 df-rn 4520 df-res 4521 df-ima 4522 df-iota 5058 df-fv 5101 df-ov 5745 df-ec 6399 |
This theorem is referenced by: caucvgprprlemval 7464 |
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