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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 |
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Ref | Expression |
---|---|
rgen3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rgen3.1 |
. . . 4
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2 | 1 | 3expa 1205 |
. . 3
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3 | 2 | ralrimiva 2567 |
. 2
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4 | 3 | rgen2 2580 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1458 ax-gen 1460 ax-4 1521 ax-17 1537 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-nf 1472 df-ral 2477 |
This theorem is referenced by: reg3exmidlemwe 4609 ltsopr 7650 ltsosr 7818 ltso 8091 aptap 8663 xrltso 9856 addcncntoplem 14700 |
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