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Mirrors > Home > ILE Home > Th. List > r19.36av | Unicode version |
Description: One direction of a restricted quantifier version of Theorem 19.36 of [Margaris] p. 90. In classical logic, the converse would hold if has at least one element, but in intuitionistic logic, that is not a sufficient condition. (Contributed by NM, 22-Oct-2003.) |
Ref | Expression |
---|---|
r19.36av |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | r19.35-1 2504 | . 2 | |
2 | idd 21 | . . . 4 | |
3 | 2 | rexlimiv 2471 | . . 3 |
4 | 3 | imim2i 12 | . 2 |
5 | 1, 4 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 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-17 1459 ax-ial 1467 ax-i5r 1468 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-ral 2353 df-rex 2354 |
This theorem is referenced by: iinss 3729 |
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