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Theorem psseq2d 4054
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
psseq2d (𝜑 → (𝐶𝐴𝐶𝐵))

Proof of Theorem psseq2d
StepHypRef Expression
1 psseq1d.1 . 2 (𝜑𝐴 = 𝐵)
2 psseq2 4049 . 2 (𝐴 = 𝐵 → (𝐶𝐴𝐶𝐵))
31, 2syl 17 1 (𝜑 → (𝐶𝐴𝐶𝐵))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205   = wceq 1542  wpss 3912
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 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-ne 2941  df-v 3446  df-in 3918  df-ss 3928  df-pss 3930
This theorem is referenced by:  psseq12d  4055  php3  9159  php3OLD  9171  inf3lem5  9573  infeq5i  9577  ackbij1lem15  10175  fin4en1  10250  chpsscon1  30488  chnle  30498  atcvatlem  31369  atcvati  31370  lsatcvat  37558
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