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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 |
Ref | Expression |
---|---|
r19.3rm |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2141 | . . 3 | |
2 | 1 | cbvexv 1836 | . 2 |
3 | eleq1 2141 | . . . 4 | |
4 | 3 | cbvexv 1836 | . . 3 |
5 | biimt 239 | . . . 4 | |
6 | df-ral 2353 | . . . . 5 | |
7 | r19.3rm.1 | . . . . . 6 | |
8 | 7 | 19.23 1608 | . . . . 5 |
9 | 6, 8 | bitri 182 | . . . 4 |
10 | 5, 9 | syl6bbr 196 | . . 3 |
11 | 4, 10 | sylbi 119 | . 2 |
12 | 2, 11 | sylbir 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 103 wal 1282 wnf 1389 wex 1421 wcel 1433 wral 2348 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-cleq 2074 df-clel 2077 df-ral 2353 |
This theorem is referenced by: r19.28m 3331 r19.3rmv 3332 r19.27m 3336 indstr 8681 |
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