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Theorem psseq2i 3839
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 3837 . 2 (𝐴 = 𝐵 → (𝐶𝐴𝐶𝐵))
31, 2ax-mp 5 1 (𝐶𝐴𝐶𝐵)
Colors of variables: wff setvar class
Syntax hints:  wb 196   = wceq 1632  wpss 3716
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-ne 2933  df-in 3722  df-ss 3729  df-pss 3731
This theorem is referenced by:  psseq12i  3840  disjpss  4172  infeq5i  8708
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