Theorem indmss 3274

Description: De Morgan's law for intersection. In classical logic, this would be equality rather than subset, as in Theorem 5.2(13') of [Stoll] p. 19. (Contributed by Jim Kingdon, 27-Jul-2018.)

Assertion

Ref	Expression
indmss	⊢ ((V ∖ 𝐴) ∪ (V ∖ 𝐵)) ⊆ (V ∖ (𝐴 ∩ 𝐵))

Proof of Theorem indmss

Step	Hyp	Ref	Expression
1		difindiss 3269	1 ⊢ ((V ∖ 𝐴) ∪ (V ∖ 𝐵)) ⊆ (V ∖ (𝐴 ∩ 𝐵))

Syntax hints:  Vcvv 2633   ∖ cdif 3010   ∪ cun 3011   ∩ cin 3012   ⊆ wss 3013

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 582  ax-in2 583  ax-io 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077

This theorem depends on definitions:  df-bi 116  df-tru 1299  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224  df-v 2635  df-dif 3015  df-un 3017  df-in 3019  df-ss 3026

This theorem is referenced by:  difdifdirss  3386