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Mirrors > Home > ILE Home > Th. List > iseqvalcbv | Unicode version |
Description: Changing the bound variables in an expression which appears in some related proofs. (Contributed by Jim Kingdon, 28-Apr-2022.) |
Ref | Expression |
---|---|
iseqvalcbv | frec frec |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq1 5833 | . . . . . . . . . 10 | |
2 | 1 | fveq2d 5474 | . . . . . . . . 9 |
3 | 2 | oveq2d 5842 | . . . . . . . 8 |
4 | oveq1 5833 | . . . . . . . 8 | |
5 | 3, 4 | cbvmpov 5903 | . . . . . . 7 |
6 | 5 | oveqi 5839 | . . . . . 6 |
7 | 6 | opeq2i 3747 | . . . . 5 |
8 | 7 | a1i 9 | . . . 4 |
9 | 8 | mpoeq3ia 5888 | . . 3 |
10 | oveq1 5833 | . . . . 5 | |
11 | oveq1 5833 | . . . . 5 | |
12 | 10, 11 | opeq12d 3751 | . . . 4 |
13 | oveq2 5834 | . . . . 5 | |
14 | 13 | opeq2d 3750 | . . . 4 |
15 | 12, 14 | cbvmpov 5903 | . . 3 |
16 | 9, 15 | eqtr3i 2180 | . 2 |
17 | freceq1 6341 | . 2 frec frec | |
18 | 16, 17 | ax-mp 5 | 1 frec frec |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1335 wcel 2128 cop 3564 cfv 5172 (class class class)co 5826 cmpo 5828 freccfrec 6339 c1 7735 caddc 7737 cuz 9444 |
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-14 2131 ax-ext 2139 ax-sep 4084 ax-pow 4137 ax-pr 4171 |
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-pw 3546 df-sn 3567 df-pr 3568 df-op 3570 df-uni 3775 df-br 3968 df-opab 4028 df-mpt 4029 df-res 4600 df-iota 5137 df-fv 5180 df-ov 5829 df-oprab 5830 df-mpo 5831 df-recs 6254 df-frec 6340 |
This theorem is referenced by: seq3-1 10368 seqf 10369 seq3p1 10370 seqf2 10372 seq1cd 10373 seqp1cd 10374 |
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