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Theorem sseq1d 3298
 Description: An equality deduction for the subclass relationship. (Contributed by NM, 14-Aug-1994.)
Hypothesis
Ref Expression
sseq1d.1 (φA = B)
Assertion
Ref Expression
sseq1d (φ → (A CB C))

Proof of Theorem sseq1d
StepHypRef Expression
1 sseq1d.1 . 2 (φA = B)
2 sseq1 3292 . 2 (A = B → (A CB C))
31, 2syl 15 1 (φ → (A CB C))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   = wceq 1642   ⊆ wss 3257 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-ss 3259 This theorem is referenced by:  sseq12d  3300  eqsstrd  3305  snssg  3844  ssiun2s  4010  elp6  4263  iotassuni  4355  dmxpss  5052  funimass1  5169  feq1  5210  fvimacnvi  5402  fvmptss  5705  clos1eq2  5875  mapsspw  6022  map0e  6023  sbthlem1  6203
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