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Mirrors > Home > ILE Home > Th. List > csbiebg | Unicode version |
Description: Bidirectional conversion between an implicit class substitution hypothesis and its explicit substitution equivalent. (Contributed by NM, 24-Mar-2013.) (Revised by Mario Carneiro, 11-Dec-2016.) |
Ref | Expression |
---|---|
csbiebg.2 |
Ref | Expression |
---|---|
csbiebg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq2 2147 | . . . 4 | |
2 | 1 | imbi1d 230 | . . 3 |
3 | 2 | albidv 1796 | . 2 |
4 | csbeq1 3001 | . . 3 | |
5 | 4 | eqeq1d 2146 | . 2 |
6 | vex 2684 | . . 3 | |
7 | csbiebg.2 | . . 3 | |
8 | 6, 7 | csbieb 3036 | . 2 |
9 | 3, 5, 8 | vtoclbg 2742 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1329 wceq 1331 wcel 1480 wnfc 2266 csb 2998 |
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 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-sbc 2905 df-csb 2999 |
This theorem is referenced by: (None) |
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