nnral - Intuitionistic Logic Explorer

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Theorem nnral 2540

Description: The double negation of a universal quantification implies the universal quantification of the double negation. Restricted quantifier version of nnal 1702. (Contributed by Jim Kingdon, 1-Aug-2024.)

**Assertion**
Ref	Expression
nnral

**Proof of Theorem nnral**
Step	Hyp	Ref	Expression
1		rexnalim 2539	. . 3
2	1	con3i 641	. 2
3		ralnex 2538	. 2
4	2, 3	sylibr 134	1

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4

wral 2528

wrex 2529

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 623 ax-in2 624 ax-5 1500 ax-gen 1502 ax-ie1 1546 ax-ie2 1547 ax-4 1563 ax-17 1579 ax-ial 1587

This theorem depends on definitions: df-bi 117 df-tru 1405 df-fal 1408 df-nf 1514 df-ral 2533 df-rex 2534

This theorem is referenced by: onntri13 7587 onntri24 7591

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