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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 3044 | . . 3 | |
2 | dfsbcq2 2950 | . . . 4 | |
3 | 2 | opabbidv 4043 | . . 3 |
4 | 1, 3 | eqeq12d 2179 | . 2 |
5 | vex 2725 | . . 3 | |
6 | nfs1v 1926 | . . . 4 | |
7 | 6 | nfopab 4045 | . . 3 |
8 | sbequ12 1758 | . . . 4 | |
9 | 8 | opabbidv 4043 | . . 3 |
10 | 5, 7, 9 | csbief 3085 | . 2 |
11 | 4, 10 | vtoclg 2782 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1342 wsb 1749 wcel 2135 wsbc 2947 csb 3041 copab 4037 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2724 df-sbc 2948 df-csb 3042 df-opab 4039 |
This theorem is referenced by: csbcnvg 4783 |
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