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Theorem sseq12d 3300
 Description: An equality deduction for the subclass relationship. (Contributed by NM, 31-May-1999.)
Hypotheses
Ref Expression
sseq1d.1 (φA = B)
sseq12d.2 (φC = D)
Assertion
Ref Expression
sseq12d (φ → (A CB D))

Proof of Theorem sseq12d
StepHypRef Expression
1 sseq1d.1 . . 3 (φA = B)
21sseq1d 3298 . 2 (φ → (A CB C))
3 sseq12d.2 . . 3 (φC = D)
43sseq2d 3299 . 2 (φ → (B CB D))
52, 4bitrd 244 1 (φ → (A CB D))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   = wceq 1642   ⊆ wss 3257 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-ss 3259 This theorem is referenced by:  3sstr3d  3313  3sstr4d  3314  ssdifeq0  3632  clos1induct  5880  frecxp  6314  frecxpg  6315
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