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Mirrors > Home > ILE Home > Th. List > csbvarg | Unicode version |
Description: The proper substitution of a class for setvar variable results in the class (if the class exists). (Contributed by NM, 10-Nov-2005.) |
Ref | Expression |
---|---|
csbvarg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2697 | . 2 | |
2 | vex 2689 | . . . . . 6 | |
3 | df-csb 3004 | . . . . . . 7 | |
4 | sbcel2gv 2972 | . . . . . . . 8 | |
5 | 4 | abbi1dv 2259 | . . . . . . 7 |
6 | 3, 5 | syl5eq 2184 | . . . . . 6 |
7 | 2, 6 | ax-mp 5 | . . . . 5 |
8 | 7 | csbeq2i 3029 | . . . 4 |
9 | csbco 3013 | . . . 4 | |
10 | df-csb 3004 | . . . 4 | |
11 | 8, 9, 10 | 3eqtr3i 2168 | . . 3 |
12 | sbcel2gv 2972 | . . . 4 | |
13 | 12 | abbi1dv 2259 | . . 3 |
14 | 11, 13 | syl5eq 2184 | . 2 |
15 | 1, 14 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wcel 1480 cab 2125 cvv 2686 wsbc 2909 csb 3003 |
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-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 |
This theorem is referenced by: sbccsb2g 3032 csbfvg 5459 f1od2 6132 bj-sels 13112 |
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