nnral - Intuitionistic Logic Explorer

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Theorem nnral 2447

Description: The double negation of a universal quantification implies the universal quantification of the double negation. Restricted quantifier version of nnal 1629. (Contributed by Jim Kingdon, 1-Aug-2024.)

**Assertion**
Ref	Expression
nnral

**Proof of Theorem nnral**
Step	Hyp	Ref	Expression
1		rexnalim 2446	. . 3
2	1	con3i 622	. 2
3		ralnex 2445	. 2
4	2, 3	sylibr 133	1

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4

wral 2435

wrex 2436

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-in1 604 ax-in2 605 ax-5 1427 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-4 1490 ax-17 1506 ax-ial 1514

This theorem depends on definitions: df-bi 116 df-tru 1338 df-fal 1341 df-nf 1441 df-ral 2440 df-rex 2441

This theorem is referenced by: onntri13 7167 onntri24 7171

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