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Mirrors > Home > ILE Home > Th. List > caucvgprprlemcbv | Unicode version |
Description: Lemma for caucvgprpr 6810. 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 3767 | . . . 4 | |
3 | fveq2 5178 | . . . . . 6 | |
4 | opeq1 3549 | . . . . . . . . . . . 12 | |
5 | 4 | eceq1d 6142 | . . . . . . . . . . 11 |
6 | 5 | fveq2d 5182 | . . . . . . . . . 10 |
7 | 6 | breq2d 3776 | . . . . . . . . 9 |
8 | 7 | abbidv 2155 | . . . . . . . 8 |
9 | 6 | breq1d 3774 | . . . . . . . . 9 |
10 | 9 | abbidv 2155 | . . . . . . . 8 |
11 | 8, 10 | opeq12d 3557 | . . . . . . 7 |
12 | 11 | oveq2d 5528 | . . . . . 6 |
13 | 3, 12 | breq12d 3777 | . . . . 5 |
14 | 3, 11 | oveq12d 5530 | . . . . . 6 |
15 | 14 | breq2d 3776 | . . . . 5 |
16 | 13, 15 | anbi12d 442 | . . . 4 |
17 | 2, 16 | imbi12d 223 | . . 3 |
18 | breq2 3768 | . . . 4 | |
19 | fveq2 5178 | . . . . . . 7 | |
20 | 19 | oveq1d 5527 | . . . . . 6 |
21 | 20 | breq2d 3776 | . . . . 5 |
22 | 19 | breq1d 3774 | . . . . 5 |
23 | 21, 22 | anbi12d 442 | . . . 4 |
24 | 18, 23 | imbi12d 223 | . . 3 |
25 | 17, 24 | cbvral2v 2541 | . 2 |
26 | 1, 25 | sylib 127 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 cab 2026 wral 2306 cop 3378 class class class wbr 3764 wf 4898 cfv 4902 (class class class)co 5512 c1o 5994 cec 6104 cnpi 6370 clti 6373 ceq 6377 crq 6382 cltq 6383 cnp 6389 cpp 6391 cltp 6393 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-br 3765 df-opab 3819 df-xp 4351 df-cnv 4353 df-dm 4355 df-rn 4356 df-res 4357 df-ima 4358 df-iota 4867 df-fv 4910 df-ov 5515 df-ec 6108 |
This theorem is referenced by: caucvgprprlemval 6786 |
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