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Mirrors > Home > ILE Home > Th. List > csbov123g | Unicode version |
Description: Move class substitution in and out of an operation. (Contributed by NM, 12-Nov-2005.) (Proof shortened by Mario Carneiro, 5-Dec-2016.) |
Ref | Expression |
---|---|
csbov123g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbeq1 3006 | . . 3 | |
2 | csbeq1 3006 | . . . 4 | |
3 | csbeq1 3006 | . . . 4 | |
4 | csbeq1 3006 | . . . 4 | |
5 | 2, 3, 4 | oveq123d 5795 | . . 3 |
6 | 1, 5 | eqeq12d 2154 | . 2 |
7 | vex 2689 | . . 3 | |
8 | nfcsb1v 3035 | . . . 4 | |
9 | nfcsb1v 3035 | . . . 4 | |
10 | nfcsb1v 3035 | . . . 4 | |
11 | 8, 9, 10 | nfov 5801 | . . 3 |
12 | csbeq1a 3012 | . . . 4 | |
13 | csbeq1a 3012 | . . . 4 | |
14 | csbeq1a 3012 | . . . 4 | |
15 | 12, 13, 14 | oveq123d 5795 | . . 3 |
16 | 7, 11, 15 | csbief 3044 | . 2 |
17 | 6, 16 | vtoclg 2746 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wcel 1480 csb 3003 (class class class)co 5774 |
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-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
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-rex 2422 df-v 2688 df-sbc 2910 df-csb 3004 df-un 3075 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-iota 5088 df-fv 5131 df-ov 5777 |
This theorem is referenced by: csbov12g 5810 |
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