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Mirrors > Home > ILE Home > Th. List > raleqbi1dv | Unicode version |
Description: Equality deduction for restricted universal quantifier. (Contributed by NM, 16-Nov-1995.) |
Ref | Expression |
---|---|
raleqd.1 |
Ref | Expression |
---|---|
raleqbi1dv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | raleq 2626 | . 2 | |
2 | raleqd.1 | . . 3 | |
3 | 2 | ralbidv 2437 | . 2 |
4 | 1, 3 | bitrd 187 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1331 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-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 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-tru 1334 df-nf 1437 df-sb 1736 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 |
This theorem is referenced by: frforeq2 4267 weeq2 4279 peano5 4512 isoeq4 5705 exmidomni 7014 pitonn 7656 peano1nnnn 7660 peano2nnnn 7661 peano5nnnn 7700 peano5nni 8723 1nn 8731 peano2nn 8732 dfuzi 9161 istopg 12166 isbasisg 12211 basis2 12215 eltg2 12222 ispsmet 12492 ismet 12513 isxmet 12514 metrest 12675 cncfval 12728 bj-indeq 13127 bj-nntrans 13149 |
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