nnal - Intuitionistic Logic Explorer

	Intuitionistic Logic Explorer		< Previous Next > Nearby theorems
Mirrors > Home > ILE Home > Th. List > nnal		Unicode version

Theorem nnal 1637

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 1634	. . 3
2	1	con3i 622	. 2
3		alnex 1487	. 2
4	2, 3	sylibr 133	1

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4

wal 1341

wex 1480

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 604 ax-in2 605 ax-5 1435 ax-gen 1437 ax-ie1 1481 ax-ie2 1482 ax-4 1498 ax-17 1514 ax-ial 1522

This theorem depends on definitions: df-bi 116 df-tru 1346 df-fal 1349 df-nf 1449

This theorem is referenced by: bj-stal 13630

W3C validator