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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 2732 | . 2 | |
2 | vex 2724 | . . . . . 6 | |
3 | df-csb 3041 | . . . . . . 7 | |
4 | sbcel2gv 3009 | . . . . . . . 8 | |
5 | 4 | abbi1dv 2284 | . . . . . . 7 |
6 | 3, 5 | syl5eq 2209 | . . . . . 6 |
7 | 2, 6 | ax-mp 5 | . . . . 5 |
8 | 7 | csbeq2i 3067 | . . . 4 |
9 | csbco 3050 | . . . 4 | |
10 | df-csb 3041 | . . . 4 | |
11 | 8, 9, 10 | 3eqtr3i 2193 | . . 3 |
12 | sbcel2gv 3009 | . . . 4 | |
13 | 12 | abbi1dv 2284 | . . 3 |
14 | 11, 13 | syl5eq 2209 | . 2 |
15 | 1, 14 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1342 wcel 2135 cab 2150 cvv 2721 wsbc 2946 csb 3040 |
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-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 df-sbc 2947 df-csb 3041 |
This theorem is referenced by: sbccsb2g 3070 csbfvg 5518 f1od2 6194 bj-sels 13637 |
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