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Mirrors > Home > ILE Home > Th. List > rexnalim | Unicode version |
Description: Relationship between restricted universal and existential quantifiers. In classical logic this would be a biconditional. (Contributed by Jim Kingdon, 17-Aug-2018.) |
Ref | Expression |
---|---|
rexnalim |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2312 |
. 2
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2 | exanaliim 1538 |
. . 3
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3 | df-ral 2311 |
. . 3
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4 | 2, 3 | sylnibr 602 |
. 2
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5 | 1, 4 | sylbi 114 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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-in1 544 ax-in2 545 ax-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-17 1419 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-fal 1249 df-nf 1350 df-ral 2311 df-rex 2312 |
This theorem is referenced by: ralexim 2318 iundif2ss 3722 |
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