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Theorem psseq1d 4057
Description: An equality deduction for the proper subclass relationship. (Contributed by NM, 9-Jun-2004.)
Hypothesis
Ref Expression
psseq1d.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
psseq1d (𝜑 → (𝐴𝐶𝐵𝐶))

Proof of Theorem psseq1d
StepHypRef Expression
1 psseq1d.1 . 2 (𝜑𝐴 = 𝐵)
2 psseq1 4052 . 2 (𝐴 = 𝐵 → (𝐴𝐶𝐵𝐶))
31, 2syl 17 1 (𝜑 → (𝐴𝐶𝐵𝐶))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205   = wceq 1542  wpss 3916
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2708
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-ne 2945  df-v 3450  df-in 3922  df-ss 3932  df-pss 3934
This theorem is referenced by:  psseq12d  4059  fin23lem32  10287  fin23lem35  10290  compssiso  10317  mrieqv2d  17526  mrissmrcd  17527  pgpfac1lem5  19865  islbs3  20632  chpsscon2  30489
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