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Mirrors > Home > ILE Home > Th. List > rgenm | Unicode version |
Description: Generalization rule that eliminates an inhabited class requirement. (Contributed by Jim Kingdon, 5-Aug-2018.) |
Ref | Expression |
---|---|
rgenm.1 |
Ref | Expression |
---|---|
rgenm |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfe1 1425 | . . . . 5 | |
2 | rgenm.1 | . . . . . 6 | |
3 | 2 | ex 113 | . . . . 5 |
4 | 1, 3 | alrimi 1455 | . . . 4 |
5 | 19.38 1606 | . . . 4 | |
6 | 4, 5 | ax-mp 7 | . . 3 |
7 | pm5.4 247 | . . . 4 | |
8 | 7 | albii 1399 | . . 3 |
9 | 6, 8 | mpbi 143 | . 2 |
10 | df-ral 2353 | . 2 | |
11 | 9, 10 | mpbir 144 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wal 1282 wex 1421 wcel 1433 wral 2348 |
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-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-4 1440 ax-ial 1467 ax-i5r 1468 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-ral 2353 |
This theorem is referenced by: (None) |
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