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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 2579 | . 2 | |
2 | idd 21 | . . . 4 | |
3 | 2 | rexlimiv 2541 | . . 3 |
4 | 3 | imim2i 12 | . 2 |
5 | 1, 4 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1480 wral 2414 wrex 2415 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-4 1487 ax-17 1506 ax-ial 1514 ax-i5r 1515 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-ral 2419 df-rex 2420 |
This theorem is referenced by: iinss 3859 |
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