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Mirrors > Home > ILE Home > Th. List > caucvgprprlemcbv | Unicode version |
Description: Lemma for caucvgprpr 7645. 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 3980 | . . . 4 | |
3 | fveq2 5481 | . . . . . 6 | |
4 | opeq1 3753 | . . . . . . . . . . . 12 | |
5 | 4 | eceq1d 6529 | . . . . . . . . . . 11 |
6 | 5 | fveq2d 5485 | . . . . . . . . . 10 |
7 | 6 | breq2d 3989 | . . . . . . . . 9 |
8 | 7 | abbidv 2282 | . . . . . . . 8 |
9 | 6 | breq1d 3987 | . . . . . . . . 9 |
10 | 9 | abbidv 2282 | . . . . . . . 8 |
11 | 8, 10 | opeq12d 3761 | . . . . . . 7 |
12 | 11 | oveq2d 5853 | . . . . . 6 |
13 | 3, 12 | breq12d 3990 | . . . . 5 |
14 | 3, 11 | oveq12d 5855 | . . . . . 6 |
15 | 14 | breq2d 3989 | . . . . 5 |
16 | 13, 15 | anbi12d 465 | . . . 4 |
17 | 2, 16 | imbi12d 233 | . . 3 |
18 | breq2 3981 | . . . 4 | |
19 | fveq2 5481 | . . . . . . 7 | |
20 | 19 | oveq1d 5852 | . . . . . 6 |
21 | 20 | breq2d 3989 | . . . . 5 |
22 | 19 | breq1d 3987 | . . . . 5 |
23 | 21, 22 | anbi12d 465 | . . . 4 |
24 | 18, 23 | imbi12d 233 | . . 3 |
25 | 17, 24 | cbvral2v 2701 | . 2 |
26 | 1, 25 | sylib 121 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 cab 2150 wral 2442 cop 3574 class class class wbr 3977 wf 5179 cfv 5183 (class class class)co 5837 c1o 6369 cec 6491 cnpi 7205 clti 7208 ceq 7212 crq 7217 cltq 7218 cnp 7224 cpp 7226 cltp 7228 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2724 df-un 3116 df-in 3118 df-ss 3125 df-sn 3577 df-pr 3578 df-op 3580 df-uni 3785 df-br 3978 df-opab 4039 df-xp 4605 df-cnv 4607 df-dm 4609 df-rn 4610 df-res 4611 df-ima 4612 df-iota 5148 df-fv 5191 df-ov 5840 df-ec 6495 |
This theorem is referenced by: caucvgprprlemval 7621 |
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