nnal - Intuitionistic Logic Explorer

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Theorem nnal 1642

Description: The double negation of a universal quantification implies the universal quantification of the double negation. (Contributed by BJ, 24-Nov-2023.)

**Assertion**
Ref	Expression
nnal

**Proof of Theorem nnal**
Step	Hyp	Ref	Expression
1		exnalim 1639	. . 3
2	1	con3i 627	. 2
3		alnex 1492	. 2
4	2, 3	sylibr 133	1

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4

wal 1346

wex 1485

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

This theorem is referenced by: bj-stal 13784

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