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Theorem psseq2i 4037
Description: An equality inference for the proper subclass relationship. (Contributed by NM, 9-Jun-2004.)
Hypothesis
Ref Expression
psseq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
psseq2i (𝐶𝐴𝐶𝐵)

Proof of Theorem psseq2i
StepHypRef Expression
1 psseq1i.1 . 2 𝐴 = 𝐵
2 psseq2 4035 . 2 (𝐴 = 𝐵 → (𝐶𝐴𝐶𝐵))
31, 2ax-mp 5 1 (𝐶𝐴𝐶𝐵)
Colors of variables: wff setvar class
Syntax hints:  wb 205   = wceq 1540  wpss 3899
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2707
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1543  df-ex 1781  df-sb 2067  df-clab 2714  df-cleq 2728  df-clel 2814  df-ne 2941  df-v 3443  df-in 3905  df-ss 3915  df-pss 3917
This theorem is referenced by:  psseq12i  4038  disjpss  4407  infeq5i  9493
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