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Mirrors > Home > ILE Home > Th. List > csbexga | Unicode version |
Description: The existence of proper substitution into a class. (Contributed by NM, 10-Nov-2005.) |
Ref | Expression |
---|---|
csbexga |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-csb 2853 | . 2 | |
2 | abid2 2158 | . . . . . . 7 | |
3 | elex 2566 | . . . . . . 7 | |
4 | 2, 3 | syl5eqel 2124 | . . . . . 6 |
5 | 4 | alimi 1344 | . . . . 5 |
6 | spsbc 2775 | . . . . 5 | |
7 | 5, 6 | syl5 28 | . . . 4 |
8 | 7 | imp 115 | . . 3 |
9 | nfcv 2178 | . . . . 5 | |
10 | 9 | sbcabel 2839 | . . . 4 |
11 | 10 | adantr 261 | . . 3 |
12 | 8, 11 | mpbid 135 | . 2 |
13 | 1, 12 | syl5eqel 2124 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wcel 1393 cab 2026 cvv 2557 wsbc 2764 csb 2852 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-sbc 2765 df-csb 2853 |
This theorem is referenced by: csbexa 3886 |
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