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Mirrors > Home > ILE Home > Th. List > cbvcsb | Unicode version |
Description: Change bound variables in a class substitution. Interestingly, this does not require any bound variable conditions on . (Contributed by Jeff Hankins, 13-Sep-2009.) (Revised by Mario Carneiro, 11-Dec-2016.) |
Ref | Expression |
---|---|
cbvcsb.1 | |
cbvcsb.2 | |
cbvcsb.3 |
Ref | Expression |
---|---|
cbvcsb |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvcsb.1 | . . . . 5 | |
2 | 1 | nfcri 2172 | . . . 4 |
3 | cbvcsb.2 | . . . . 5 | |
4 | 3 | nfcri 2172 | . . . 4 |
5 | cbvcsb.3 | . . . . 5 | |
6 | 5 | eleq2d 2107 | . . . 4 |
7 | 2, 4, 6 | cbvsbc 2791 | . . 3 |
8 | 7 | abbii 2153 | . 2 |
9 | df-csb 2853 | . 2 | |
10 | df-csb 2853 | . 2 | |
11 | 8, 9, 10 | 3eqtr4i 2070 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1243 wcel 1393 cab 2026 wnfc 2165 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-sbc 2765 df-csb 2853 |
This theorem is referenced by: cbvcsbv 2857 |
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