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Theorem psseq2d 3850
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 3845 . 2 (𝐴 = 𝐵 → (𝐶𝐴𝐶𝐵))
31, 2syl 17 1 (𝜑 → (𝐶𝐴𝐶𝐵))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196   = wceq 1631  wpss 3724
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-ext 2751
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-clab 2758  df-cleq 2764  df-clel 2767  df-ne 2944  df-in 3730  df-ss 3737  df-pss 3739
This theorem is referenced by:  psseq12d  3851  php3  8306  inf3lem5  8697  infeq5i  8701  ackbij1lem15  9262  fin4en1  9337  chpsscon1  28703  chnle  28713  atcvatlem  29584  atcvati  29585  lsatcvat  34857
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