nnral - Intuitionistic Logic Explorer

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

Theorem nnral 2523

Description: The double negation of a universal quantification implies the universal quantification of the double negation. Restricted quantifier version of nnal 1698. (Contributed by Jim Kingdon, 1-Aug-2024.)

**Assertion**
Ref	Expression
nnral

**Proof of Theorem nnral**
Step	Hyp	Ref	Expression
1		rexnalim 2522	. . 3
2	1	con3i 637	. 2
3		ralnex 2521	. 2
4	2, 3	sylibr 134	1

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4

wral 2511

wrex 2512

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 df-ral 2516 df-rex 2517

This theorem is referenced by: onntri13 7516 onntri24 7520

W3C validator