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Mirrors > Home > ILE Home > Th. List > rgen3 | Unicode version |
Description: Generalization rule for restricted quantification. (Contributed by NM, 12-Jan-2008.) |
Ref | Expression |
---|---|
rgen3.1 |
Ref | Expression |
---|---|
rgen3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rgen3.1 | . . . 4 | |
2 | 1 | 3expa 1104 | . . 3 |
3 | 2 | ralrimiva 2392 | . 2 |
4 | 3 | rgen2 2405 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 w3a 885 wcel 1393 wral 2306 |
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-5 1336 ax-gen 1338 ax-4 1400 ax-17 1419 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-nf 1350 df-ral 2311 |
This theorem is referenced by: reg3exmidlemwe 4303 ltsopr 6694 ltsosr 6849 ltso 7096 xrltso 8717 |
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