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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 5781 | . . . . . . . . . 10 | |
2 | 1 | fveq2d 5425 | . . . . . . . . 9 |
3 | 2 | oveq2d 5790 | . . . . . . . 8 |
4 | oveq1 5781 | . . . . . . . 8 | |
5 | 3, 4 | cbvmpov 5851 | . . . . . . 7 |
6 | 5 | oveqi 5787 | . . . . . 6 |
7 | 6 | opeq2i 3709 | . . . . 5 |
8 | 7 | a1i 9 | . . . 4 |
9 | 8 | mpoeq3ia 5836 | . . 3 |
10 | oveq1 5781 | . . . . 5 | |
11 | oveq1 5781 | . . . . 5 | |
12 | 10, 11 | opeq12d 3713 | . . . 4 |
13 | oveq2 5782 | . . . . 5 | |
14 | 13 | opeq2d 3712 | . . . 4 |
15 | 12, 14 | cbvmpov 5851 | . . 3 |
16 | 9, 15 | eqtr3i 2162 | . 2 |
17 | freceq1 6289 | . 2 frec frec | |
18 | 16, 17 | ax-mp 5 | 1 frec frec |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1331 wcel 1480 cop 3530 cfv 5123 (class class class)co 5774 cmpo 5776 freccfrec 6287 c1 7621 caddc 7623 cuz 9326 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-opab 3990 df-mpt 3991 df-res 4551 df-iota 5088 df-fv 5131 df-ov 5777 df-oprab 5778 df-mpo 5779 df-recs 6202 df-frec 6288 |
This theorem is referenced by: seq3-1 10233 seqf 10234 seq3p1 10235 seqf2 10237 seq1cd 10238 seqp1cd 10239 |
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