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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 2100 |
. . 3
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2 | 1 | cbvexv 1795 |
. 2
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3 | eleq1 2100 |
. . . 4
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4 | 3 | cbvexv 1795 |
. . 3
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5 | biimt 230 |
. . . 4
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6 | df-ral 2311 |
. . . . 5
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7 | r19.3rm.1 |
. . . . . 6
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8 | 7 | 19.23 1568 |
. . . . 5
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9 | 6, 8 | bitri 173 |
. . . 4
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10 | 5, 9 | syl6bbr 187 |
. . 3
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11 | 4, 10 | sylbi 114 |
. 2
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12 | 2, 11 | sylbir 125 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-cleq 2033 df-clel 2036 df-ral 2311 |
This theorem is referenced by: r19.28m 3311 r19.3rmv 3312 r19.27m 3316 indstr 8536 |
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