nnal - Intuitionistic Logic Explorer

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Theorem nnal 1672

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 1669	. . 3
2	1	con3i 633	. 2
3		alnex 1522	. 2
4	2, 3	sylibr 134	1

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4

wal 1371

wex 1515

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

This theorem is referenced by: bj-stal 15685

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