nnal - Intuitionistic Logic Explorer

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Theorem nnal 1698

Description: The double negation of a universal quantification implies the universal quantification of the double negation. The converse holds in classical but not in intuitionistic logic. (Contributed by BJ, 24-Nov-2023.)

**Assertion**
Ref	Expression
nnal

**Proof of Theorem nnal**
Step	Hyp	Ref	Expression
1		exnalim 1695	. . 3
2	1	con3i 637	. 2
3		alnex 1548	. 2
4	2, 3	sylibr 134	1

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4

wal 1396

wex 1541

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 619 ax-in2 620 ax-5 1496 ax-gen 1498 ax-ie1 1542 ax-ie2 1543 ax-4 1559 ax-17 1575 ax-ial 1583

This theorem depends on definitions: df-bi 117 df-tru 1401 df-fal 1404 df-nf 1510

This theorem is referenced by: bj-stal 16467

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