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Theorem psseq1d 4092
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 4087 . 2 (𝐴 = 𝐵 → (𝐴𝐶𝐵𝐶))
31, 2syl 17 1 (𝜑 → (𝐴𝐶𝐵𝐶))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205   = wceq 1533  wpss 3950
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2706  df-cleq 2720  df-clel 2806  df-ne 2938  df-v 3475  df-in 3956  df-ss 3966  df-pss 3968
This theorem is referenced by:  psseq12d  4094  fin23lem32  10375  fin23lem35  10378  compssiso  10405  mrieqv2d  17626  mrissmrcd  17627  pgpfac1lem5  20043  islbs3  21050  chpsscon2  31335
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