Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 2911 | . . 3 | |
2 | dfsbcq2 2818 | . . . 4 | |
3 | 2 | opabbidv 3844 | . . 3 |
4 | 1, 3 | eqeq12d 2095 | . 2 |
5 | vex 2604 | . . 3 | |
6 | nfs1v 1856 | . . . 4 | |
7 | 6 | nfopab 3846 | . . 3 |
8 | sbequ12 1694 | . . . 4 | |
9 | 8 | opabbidv 3844 | . . 3 |
10 | 5, 7, 9 | csbief 2947 | . 2 |
11 | 4, 10 | vtoclg 2658 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1284 wcel 1433 wsb 1685 wsbc 2815 csb 2908 copab 3838 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-v 2603 df-sbc 2816 df-csb 2909 df-opab 3840 |
This theorem is referenced by: csbcnvg 4537 |
Copyright terms: Public domain | W3C validator |