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Mirrors > Home > ILE Home > Th. List > raleqdv | Unicode version |
Description: Equality deduction for restricted universal quantifier. (Contributed by NM, 13-Nov-2005.) |
Ref | Expression |
---|---|
raleq1d.1 |
Ref | Expression |
---|---|
raleqdv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | raleq1d.1 | . 2 | |
2 | raleq 2505 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wceq 1243 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-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 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-tru 1246 df-nf 1350 df-sb 1646 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 |
This theorem is referenced by: raleqbidv 2517 raleqbidva 2519 cbvfo 5425 isoselem 5459 ofrfval 5720 issmo2 5904 smoeq 5905 tfrlemisucaccv 5939 fzrevral2 8968 fzrevral3 8969 fzshftral 8970 fzoshftral 9094 caucvgre 9580 cvg1nlemres 9584 rexuz3 9588 resqrexlemoverl 9619 resqrexlemsqa 9622 resqrexlemex 9623 climconst 9811 climshftlemg 9823 serif0 9871 |
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