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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 2100 | . . 3 | |
2 | 1 | cbvexv 1795 | . 2 |
3 | eleq1 2100 | . . . 4 | |
4 | 3 | cbvexv 1795 | . . 3 |
5 | biimt 230 | . . . 4 | |
6 | df-ral 2311 | . . . . 5 | |
7 | r19.3rm.1 | . . . . . 6 | |
8 | 7 | 19.23 1568 | . . . . 5 |
9 | 6, 8 | bitri 173 | . . . 4 |
10 | 5, 9 | syl6bbr 187 | . . 3 |
11 | 4, 10 | sylbi 114 | . 2 |
12 | 2, 11 | sylbir 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wal 1241 wnf 1349 wex 1381 wcel 1393 wral 2306 |
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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