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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 |
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Ref | Expression |
---|---|
raleqbi1dv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | raleq 2672 |
. 2
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2 | raleqd.1 |
. . 3
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3 | 2 | ralbidv 2477 |
. 2
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4 | 1, 3 | bitrd 188 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 |
This theorem is referenced by: frforeq2 4345 weeq2 4357 peano5 4597 isoeq4 5804 exmidomni 7139 tapeq2 7251 pitonn 7846 peano1nnnn 7850 peano2nnnn 7851 peano5nnnn 7890 peano5nni 8920 1nn 8928 peano2nn 8929 dfuzi 9361 mhmpropd 12811 issubm 12817 iscmn 13049 istopg 13390 isbasisg 13435 basis2 13439 eltg2 13446 ispsmet 13716 ismet 13737 isxmet 13738 metrest 13899 cncfval 13952 bj-indeq 14563 bj-nntrans 14585 |
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