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Theorem sseq12i 3664
Description: An equality inference for the subclass relationship. (Contributed by NM, 31-May-1999.) (Proof shortened by Eric Schmidt, 26-Jan-2007.)
Hypotheses
Ref Expression
sseq1i.1 𝐴 = 𝐵
sseq12i.2 𝐶 = 𝐷
Assertion
Ref Expression
sseq12i (𝐴𝐶𝐵𝐷)

Proof of Theorem sseq12i
StepHypRef Expression
1 sseq1i.1 . 2 𝐴 = 𝐵
2 sseq12i.2 . 2 𝐶 = 𝐷
3 sseq12 3661 . 2 ((𝐴 = 𝐵𝐶 = 𝐷) → (𝐴𝐶𝐵𝐷))
41, 2, 3mp2an 708 1 (𝐴𝐶𝐵𝐷)
Colors of variables: wff setvar class
Syntax hints:  wb 196   = wceq 1523  wss 3607
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-in 3614  df-ss 3621
This theorem is referenced by:  3sstr3i  3676  3sstr4i  3677  3sstr3g  3678  3sstr4g  3679  ss2rab  3711  rabsssn  4247  issubgr  26208  pjordi  29160  mdsldmd1i  29318  iuninc  29505  cvmlift2lem12  31422  brtrclfv2  38336  nzss  38833  hoidmvle  41135  ovolval5lem3  41189  fldhmsubc  42409  fldhmsubcALTV  42427
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