nnral - Intuitionistic Logic Explorer

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Theorem nnral 2460

Description: The double negation of a universal quantification implies the universal quantification of the double negation. Restricted quantifier version of nnal 1642. (Contributed by Jim Kingdon, 1-Aug-2024.)

**Assertion**
Ref	Expression
nnral

**Proof of Theorem nnral**
Step	Hyp	Ref	Expression
1		rexnalim 2459	. . 3
2	1	con3i 627	. 2
3		ralnex 2458	. 2
4	2, 3	sylibr 133	1

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4

wral 2448

wrex 2449

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 609 ax-in2 610 ax-5 1440 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-4 1503 ax-17 1519 ax-ial 1527

This theorem depends on definitions: df-bi 116 df-tru 1351 df-fal 1354 df-nf 1454 df-ral 2453 df-rex 2454

This theorem is referenced by: onntri13 7215 onntri24 7219

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