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Mirrors > Home > ILE Home > Th. List > 3gencl | Unicode version |
Description: Implicit substitution for class with embedded variable. (Contributed by NM, 17-May-1996.) |
Ref | Expression |
---|---|
3gencl.1 | |
3gencl.2 | |
3gencl.3 | |
3gencl.4 | |
3gencl.5 | |
3gencl.6 | |
3gencl.7 |
Ref | Expression |
---|---|
3gencl |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3gencl.3 | . . . . 5 | |
2 | df-rex 2312 | . . . . 5 | |
3 | 1, 2 | bitri 173 | . . . 4 |
4 | 3gencl.6 | . . . . 5 | |
5 | 4 | imbi2d 219 | . . . 4 |
6 | 3gencl.1 | . . . . . 6 | |
7 | 3gencl.2 | . . . . . 6 | |
8 | 3gencl.4 | . . . . . . 7 | |
9 | 8 | imbi2d 219 | . . . . . 6 |
10 | 3gencl.5 | . . . . . . 7 | |
11 | 10 | imbi2d 219 | . . . . . 6 |
12 | 3gencl.7 | . . . . . . 7 | |
13 | 12 | 3expia 1106 | . . . . . 6 |
14 | 6, 7, 9, 11, 13 | 2gencl 2587 | . . . . 5 |
15 | 14 | com12 27 | . . . 4 |
16 | 3, 5, 15 | gencl 2586 | . . 3 |
17 | 16 | com12 27 | . 2 |
18 | 17 | 3impia 1101 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 w3a 885 wceq 1243 wex 1381 wcel 1393 wrex 2307 |
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-gen 1338 ax-ie2 1383 ax-17 1419 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-rex 2312 |
This theorem is referenced by: axpre-ltwlin 6957 axpre-lttrn 6958 axpre-ltadd 6960 axpre-mulext 6962 |
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