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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 1181 | . . 3 |
3 | 2 | ralrimiva 2503 | . 2 |
4 | 3 | rgen2 2516 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 962 wcel 1480 wral 2414 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1423 ax-gen 1425 ax-4 1487 ax-17 1506 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-nf 1437 df-ral 2419 |
This theorem is referenced by: reg3exmidlemwe 4488 ltsopr 7397 ltsosr 7565 ltso 7835 xrltso 9575 addcncntoplem 12709 |
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