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Mirrors > Home > ILE Home > Th. List > r19.3rm | Unicode version |
Description: Restricted quantification of wff not containing quantified variable. (Contributed by Jim Kingdon, 19-Dec-2018.) |
Ref | Expression |
---|---|
r19.3rm.1 |
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Ref | Expression |
---|---|
r19.3rm |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2203 |
. . 3
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2 | 1 | cbvexv 1891 |
. 2
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3 | eleq1 2203 |
. . . 4
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4 | 3 | cbvexv 1891 |
. . 3
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5 | biimt 240 |
. . . 4
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6 | df-ral 2422 |
. . . . 5
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7 | r19.3rm.1 |
. . . . . 6
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8 | 7 | 19.23 1657 |
. . . . 5
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9 | 6, 8 | bitri 183 |
. . . 4
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10 | 5, 9 | syl6bbr 197 |
. . 3
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11 | 4, 10 | sylbi 120 |
. 2
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12 | 2, 11 | sylbir 134 |
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 105 ax-ia2 106 ax-ia3 107 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-cleq 2133 df-clel 2136 df-ral 2422 |
This theorem is referenced by: r19.28m 3457 r19.3rmv 3458 r19.27m 3463 indstr 9415 |
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