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Theorem ssun4 3887
 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 3885 . 2 𝐵 ⊆ (𝐶𝐵)
2 sstr2 3716 . 2 (𝐴𝐵 → (𝐵 ⊆ (𝐶𝐵) → 𝐴 ⊆ (𝐶𝐵)))
31, 2mpi 20 1 (𝐴𝐵𝐴 ⊆ (𝐶𝐵))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∪ cun 3678   ⊆ wss 3680 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1835  ax-4 1850  ax-5 1952  ax-6 2018  ax-7 2054  ax-9 2112  ax-10 2132  ax-11 2147  ax-12 2160  ax-13 2355  ax-ext 2704 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1599  df-ex 1818  df-nf 1823  df-sb 2011  df-clab 2711  df-cleq 2717  df-clel 2720  df-nfc 2855  df-v 3306  df-un 3685  df-in 3687  df-ss 3694 This theorem is referenced by:  ssun  3900  xpsspw  5341  uncmp  21329  volcn  23495  bnj1408  31332  bnj1452  31348  dftrpred3g  31959  elrfi  37676  cnvrcl0  38351
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