Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 2566 | . 2 | |
2 | vex 2560 | . . . . . 6 | |
3 | df-csb 2853 | . . . . . . 7 | |
4 | sbcel2gv 2822 | . . . . . . . 8 | |
5 | 4 | abbi1dv 2157 | . . . . . . 7 |
6 | 3, 5 | syl5eq 2084 | . . . . . 6 |
7 | 2, 6 | ax-mp 7 | . . . . 5 |
8 | 7 | csbeq2i 2876 | . . . 4 |
9 | csbco 2861 | . . . 4 | |
10 | df-csb 2853 | . . . 4 | |
11 | 8, 9, 10 | 3eqtr3i 2068 | . . 3 |
12 | sbcel2gv 2822 | . . . 4 | |
13 | 12 | abbi1dv 2157 | . . 3 |
14 | 11, 13 | syl5eq 2084 | . 2 |
15 | 1, 14 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1243 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: sbccsb2g 2879 csbfvg 5211 bj-sels 10034 |
Copyright terms: Public domain | W3C validator |