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Mirrors > Home > ILE Home > Th. List > 2gencl | Unicode version |
Description: Implicit substitution for class with embedded variable. (Contributed by NM, 17-May-1996.) |
Ref | Expression |
---|---|
2gencl.1 | |
2gencl.2 | |
2gencl.3 | |
2gencl.4 | |
2gencl.5 |
Ref | Expression |
---|---|
2gencl |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2gencl.2 | . . . 4 | |
2 | df-rex 2354 | . . . 4 | |
3 | 1, 2 | bitri 182 | . . 3 |
4 | 2gencl.4 | . . . 4 | |
5 | 4 | imbi2d 228 | . . 3 |
6 | 2gencl.1 | . . . . . 6 | |
7 | df-rex 2354 | . . . . . 6 | |
8 | 6, 7 | bitri 182 | . . . . 5 |
9 | 2gencl.3 | . . . . . 6 | |
10 | 9 | imbi2d 228 | . . . . 5 |
11 | 2gencl.5 | . . . . . 6 | |
12 | 11 | ex 113 | . . . . 5 |
13 | 8, 10, 12 | gencl 2631 | . . . 4 |
14 | 13 | com12 30 | . . 3 |
15 | 3, 5, 14 | gencl 2631 | . 2 |
16 | 15 | impcom 123 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wceq 1284 wex 1421 wcel 1433 wrex 2349 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-gen 1378 ax-ie2 1423 ax-17 1459 |
This theorem depends on definitions: df-bi 115 df-rex 2354 |
This theorem is referenced by: 3gencl 2633 axaddrcl 7033 axmulrcl 7035 axpre-apti 7051 axpre-mulgt0 7053 uzin2 9873 |
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