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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 2202 | . . 3 | |
2 | 1 | cbvexv 1890 | . 2 |
3 | eleq1 2202 | . . . 4 | |
4 | 3 | cbvexv 1890 | . . 3 |
5 | biimt 240 | . . . 4 | |
6 | df-ral 2421 | . . . . 5 | |
7 | r19.3rm.1 | . . . . . 6 | |
8 | 7 | 19.23 1656 | . . . . 5 |
9 | 6, 8 | bitri 183 | . . . 4 |
10 | 5, 9 | syl6bbr 197 | . . 3 |
11 | 4, 10 | sylbi 120 | . 2 |
12 | 2, 11 | sylbir 134 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1329 wnf 1436 wex 1468 wcel 1480 wral 2416 |
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 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-cleq 2132 df-clel 2135 df-ral 2421 |
This theorem is referenced by: r19.28m 3452 r19.3rmv 3453 r19.27m 3458 indstr 9388 |
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