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Theorem ssun4 4034
 Description: Subclass law for union of classes. (Contributed by NM, 14-Aug-1994.)
Assertion
Ref Expression
ssun4 (𝐴𝐵𝐴 ⊆ (𝐶𝐵))

Proof of Theorem ssun4
StepHypRef Expression
1 ssun2 4032 . 2 𝐵 ⊆ (𝐶𝐵)
2 sstr2 3859 . 2 (𝐴𝐵 → (𝐵 ⊆ (𝐶𝐵) → 𝐴 ⊆ (𝐶𝐵)))
31, 2mpi 20 1 (𝐴𝐵𝐴 ⊆ (𝐶𝐵))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∪ cun 3821   ⊆ wss 3823 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1965  ax-8 2052  ax-9 2059  ax-10 2079  ax-11 2093  ax-12 2106  ax-ext 2744 This theorem depends on definitions:  df-bi 199  df-an 388  df-or 834  df-tru 1510  df-ex 1743  df-nf 1747  df-sb 2016  df-clab 2753  df-cleq 2765  df-clel 2840  df-nfc 2912  df-v 3411  df-un 3828  df-in 3830  df-ss 3837 This theorem is referenced by:  ssun  4047  xpsspw  5528  uncmp  21727  volcn  23922  bnj1408  31982  bnj1452  31998  dftrpred3g  32622  pibt2  34168  elrfi  38715  cnvrcl0  39377
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