nnral - Intuitionistic Logic Explorer

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Theorem nnral 2456

Description: The double negation of a universal quantification implies the universal quantification of the double negation. Restricted quantifier version of nnal 1637. (Contributed by Jim Kingdon, 1-Aug-2024.)

**Assertion**
Ref	Expression
nnral

**Proof of Theorem nnral**
Step	Hyp	Ref	Expression
1		rexnalim 2455	. . 3
2	1	con3i 622	. 2
3		ralnex 2454	. 2
4	2, 3	sylibr 133	1

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4

wral 2444

wrex 2445

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 1435 ax-gen 1437 ax-ie1 1481 ax-ie2 1482 ax-4 1498 ax-17 1514 ax-ial 1522

This theorem depends on definitions: df-bi 116 df-tru 1346 df-fal 1349 df-nf 1449 df-ral 2449 df-rex 2450

This theorem is referenced by: onntri13 7194 onntri24 7198

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