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Theorem sseq12i 4011
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 4008 . 2 ((𝐴 = 𝐵𝐶 = 𝐷) → (𝐴𝐶𝐵𝐷))
41, 2, 3mp2an 688 1 (𝐴𝐶𝐵𝐷)
Colors of variables: wff setvar class
Syntax hints:  wb 205   = wceq 1539  wss 3947
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1911  ax-6 1969  ax-7 2009  ax-8 2106  ax-9 2114  ax-ext 2701
This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1542  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2722  df-clel 2808  df-v 3474  df-in 3954  df-ss 3964
This theorem is referenced by:  3sstr3i  4023  3sstr4i  4024  3sstr3g  4025  3sstr4g  4026  ss2rab  4067  rabsssn  4669  issubgr  28795  pjordi  31693  mdsldmd1i  31851  iuninc  32059  cvmlift2lem12  34603  brtrclfv2  42780  nzss  43378  hoidmvle  45614  fldhmsubc  47070  fldhmsubcALTV  47088
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