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Mirrors > Home > ILE Home > Th. List > csbopabg | Unicode version |
Description: Move substitution into a class abstraction. (Contributed by NM, 6-Aug-2007.) (Proof shortened by Mario Carneiro, 17-Nov-2016.) |
Ref | Expression |
---|---|
csbopabg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbeq1 3006 | . . 3 | |
2 | dfsbcq2 2912 | . . . 4 | |
3 | 2 | opabbidv 3994 | . . 3 |
4 | 1, 3 | eqeq12d 2154 | . 2 |
5 | vex 2689 | . . 3 | |
6 | nfs1v 1912 | . . . 4 | |
7 | 6 | nfopab 3996 | . . 3 |
8 | sbequ12 1744 | . . . 4 | |
9 | 8 | opabbidv 3994 | . . 3 |
10 | 5, 7, 9 | csbief 3044 | . 2 |
11 | 4, 10 | vtoclg 2746 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wcel 1480 wsb 1735 wsbc 2909 csb 3003 copab 3988 |
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-v 2688 df-sbc 2910 df-csb 3004 df-opab 3990 |
This theorem is referenced by: csbcnvg 4723 |
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