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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 5860 | . . . . . . . . . 10 | |
2 | 1 | fveq2d 5500 | . . . . . . . . 9 |
3 | 2 | oveq2d 5869 | . . . . . . . 8 |
4 | oveq1 5860 | . . . . . . . 8 | |
5 | 3, 4 | cbvmpov 5933 | . . . . . . 7 |
6 | 5 | oveqi 5866 | . . . . . 6 |
7 | 6 | opeq2i 3769 | . . . . 5 |
8 | 7 | a1i 9 | . . . 4 |
9 | 8 | mpoeq3ia 5918 | . . 3 |
10 | oveq1 5860 | . . . . 5 | |
11 | oveq1 5860 | . . . . 5 | |
12 | 10, 11 | opeq12d 3773 | . . . 4 |
13 | oveq2 5861 | . . . . 5 | |
14 | 13 | opeq2d 3772 | . . . 4 |
15 | 12, 14 | cbvmpov 5933 | . . 3 |
16 | 9, 15 | eqtr3i 2193 | . 2 |
17 | freceq1 6371 | . 2 frec frec | |
18 | 16, 17 | ax-mp 5 | 1 frec frec |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1348 wcel 2141 cop 3586 cfv 5198 (class class class)co 5853 cmpo 5855 freccfrec 6369 c1 7775 caddc 7777 cuz 9487 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-uni 3797 df-br 3990 df-opab 4051 df-mpt 4052 df-res 4623 df-iota 5160 df-fv 5206 df-ov 5856 df-oprab 5857 df-mpo 5858 df-recs 6284 df-frec 6370 |
This theorem is referenced by: seq3-1 10416 seqf 10417 seq3p1 10418 seqf2 10420 seq1cd 10421 seqp1cd 10422 |
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