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Mirrors > Home > ILE Home > Th. List > exanaliim | Unicode version |
Description: A transformation of quantifiers and logical connectives. In classical logic the converse also holds. (Contributed by Jim Kingdon, 15-Jul-2018.) |
Ref | Expression |
---|---|
exanaliim |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | annimim 782 | . . 3 | |
2 | 1 | eximi 1491 | . 2 |
3 | exnalim 1537 | . 2 | |
4 | 2, 3 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wal 1241 wex 1381 |
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 |
This theorem is referenced by: rexnalim 2317 nssr 3003 nssssr 3958 brprcneu 5171 |
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