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Theorem psseq2i 4103
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 4101 . 2 (𝐴 = 𝐵 → (𝐶𝐴𝐶𝐵))
31, 2ax-mp 5 1 (𝐶𝐴𝐶𝐵)
Colors of variables: wff setvar class
Syntax hints:  wb 206   = wceq 1537  wpss 3964
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1777  df-cleq 2727  df-ne 2939  df-ss 3980  df-pss 3983
This theorem is referenced by:  psseq12i  4104  disjpss  4467  infeq5i  9674
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