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Mirrors > Home > ILE Home > Th. List > r19.37 | Unicode version |
Description: Restricted version of one direction of Theorem 19.37 of [Margaris] p. 90. In classical logic the converse would hold if has at least one element, but that is not sufficient in intuitionistic logic. (Contributed by FL, 13-May-2012.) (Revised by Mario Carneiro, 11-Dec-2016.) |
Ref | Expression |
---|---|
r19.37.1 |
Ref | Expression |
---|---|
r19.37 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | r19.37.1 | . . 3 | |
2 | ax-1 5 | . . 3 | |
3 | 1, 2 | ralrimi 2432 | . 2 |
4 | r19.35-1 2504 | . 2 | |
5 | 3, 4 | syl5 32 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wnf 1389 wcel 1433 wral 2348 wrex 2349 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-4 1440 ax-ial 1467 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-ral 2353 df-rex 2354 |
This theorem is referenced by: r19.37av 2507 |
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