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Theorem psseq1d 3697
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 3692 . 2 (𝐴 = 𝐵 → (𝐴𝐶𝐵𝐶))
31, 2syl 17 1 (𝜑 → (𝐴𝐶𝐵𝐶))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196   = wceq 1482  wpss 3573
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1721  ax-4 1736  ax-5 1838  ax-6 1887  ax-7 1934  ax-9 1998  ax-10 2018  ax-11 2033  ax-12 2046  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1485  df-ex 1704  df-nf 1709  df-sb 1880  df-clab 2608  df-cleq 2614  df-clel 2617  df-ne 2794  df-in 3579  df-ss 3586  df-pss 3588
This theorem is referenced by:  psseq12d  3699  fin23lem32  9163  fin23lem35  9166  compssiso  9193  mrieqv2d  16293  mrissmrcd  16294  pgpfac1lem5  18472  islbs3  19149  chpsscon2  28348
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