undm - New Foundations Explorer

	New Foundations Explorer		< Previous Next > Nearby theorems
Mirrors > Home > NFE Home > Th. List > undm		GIF version

Theorem undm 3512

Description: De Morgan's law for union. Theorem 5.2(13) of [Stoll] p. 19. (Contributed by NM, 18-Aug-2004.)

**Assertion**
Ref	Expression
undm	⊢ (V ∖ (A ∪ B)) = ((V ∖ A) ∩ (V ∖ B))

**Proof of Theorem undm**
Step	Hyp	Ref	Expression
1		difundi 3507	1 ⊢ (V ∖ (A ∪ B)) = ((V ∖ A) ∩ (V ∖ B))

Colors of variables: wff setvar class

Syntax hints: = wceq 1642 Vcvv 2859 ∖ cdif 3206 ∪ cun 3207 ∩ cin 3208

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334

This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-un 3214 df-dif 3215

This theorem is referenced by: difun1 3514