nnral - Intuitionistic Logic Explorer

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Theorem nnral 2496

Description: The double negation of a universal quantification implies the universal quantification of the double negation. Restricted quantifier version of nnal 1672. (Contributed by Jim Kingdon, 1-Aug-2024.)

**Assertion**
Ref	Expression
nnral

**Proof of Theorem nnral**
Step	Hyp	Ref	Expression
1		rexnalim 2495	. . 3
2	1	con3i 633	. 2
3		ralnex 2494	. 2
4	2, 3	sylibr 134	1

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4

wral 2484

wrex 2485

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-5 1470 ax-gen 1472 ax-ie1 1516 ax-ie2 1517 ax-4 1533 ax-17 1549 ax-ial 1557

This theorem depends on definitions: df-bi 117 df-tru 1376 df-fal 1379 df-nf 1484 df-ral 2489 df-rex 2490

This theorem is referenced by: onntri13 7350 onntri24 7354

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