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Theorem psseq2d 4002
 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 3997 . 2 (𝐴 = 𝐵 → (𝐶𝐴𝐶𝐵))
31, 2syl 17 1 (𝜑 → (𝐶𝐴𝐶𝐵))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 209   = wceq 1539   ⊊ wpss 3862 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 1912  ax-6 1971  ax-7 2016  ax-8 2114  ax-9 2122  ax-ext 2730 This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1542  df-ex 1783  df-sb 2071  df-clab 2737  df-cleq 2751  df-clel 2831  df-ne 2953  df-v 3412  df-in 3868  df-ss 3878  df-pss 3880 This theorem is referenced by:  psseq12d  4003  php3  8739  inf3lem5  9142  infeq5i  9146  ackbij1lem15  9708  fin4en1  9783  chpsscon1  29401  chnle  29411  atcvatlem  30282  atcvati  30283  lsatcvat  36662
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