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Mirrors > Home > ILE Home > Th. List > r19.9rmv | Unicode version |
Description: Restricted quantification of wff not containing quantified variable. (Contributed by Jim Kingdon, 5-Aug-2018.) |
Ref | Expression |
---|---|
r19.9rmv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2240 |
. . 3
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2 | 1 | cbvexv 1918 |
. 2
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3 | eleq1 2240 |
. . . 4
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4 | 3 | cbvexv 1918 |
. . 3
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5 | df-rex 2461 |
. . . . 5
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6 | 19.41v 1902 |
. . . . 5
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7 | 5, 6 | bitri 184 |
. . . 4
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8 | 7 | baibr 920 |
. . 3
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9 | 4, 8 | sylbi 121 |
. 2
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10 | 2, 9 | sylbir 135 |
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 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-cleq 2170 df-clel 2173 df-rex 2461 |
This theorem is referenced by: r19.45mv 3516 r19.44mv 3517 iunconstm 3894 fconstfvm 5733 frecabcl 6397 ltexprlemloc 7603 lcmgcdlem 12069 dvdsr02 13205 |
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