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Mirrors > Home > ILE Home > Th. List > ralidm | Unicode version |
Description: Idempotent law for restricted quantifier. (Contributed by NM, 28-Mar-1997.) |
Ref | Expression |
---|---|
ralidm |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfra1 2501 | . . 3 | |
2 | anidm 394 | . . . 4 | |
3 | rsp2 2520 | . . . 4 | |
4 | 2, 3 | syl5bir 152 | . . 3 |
5 | 1, 4 | ralrimi 2541 | . 2 |
6 | ax-1 6 | . . . 4 | |
7 | nfra1 2501 | . . . . 5 | |
8 | 7 | 19.23 1671 | . . . 4 |
9 | 6, 8 | sylibr 133 | . . 3 |
10 | df-ral 2453 | . . 3 | |
11 | 9, 10 | sylibr 133 | . 2 |
12 | 5, 11 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1346 wex 1485 wcel 2141 wral 2448 |
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 1440 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-4 1503 ax-ial 1527 ax-i5r 1528 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-ral 2453 |
This theorem is referenced by: issref 4991 cnvpom 5151 |
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