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Theorem psseq2d 3986
 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 3981 . 2 (𝐴 = 𝐵 → (𝐶𝐴𝐶𝐵))
31, 2syl 17 1 (𝜑 → (𝐶𝐴𝐶𝐵))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 207   = wceq 1520   ⊊ wpss 3855 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1775  ax-4 1789  ax-5 1886  ax-6 1945  ax-7 1990  ax-8 2081  ax-9 2089  ax-10 2110  ax-11 2124  ax-12 2139  ax-ext 2767 This theorem depends on definitions:  df-bi 208  df-an 397  df-or 843  df-tru 1523  df-ex 1760  df-nf 1764  df-sb 2041  df-clab 2774  df-cleq 2786  df-clel 2861  df-ne 2983  df-in 3861  df-ss 3869  df-pss 3871 This theorem is referenced by:  psseq12d  3987  php3  8540  inf3lem5  8930  infeq5i  8934  ackbij1lem15  9491  fin4en1  9566  chpsscon1  28960  chnle  28970  atcvatlem  29841  atcvati  29842  lsatcvat  35667
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