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Theorem psseq12i 3923
Description: An equality inference for the proper subclass relationship. (Contributed by NM, 9-Jun-2004.)
Hypotheses
Ref Expression
psseq1i.1 𝐴 = 𝐵
psseq12i.2 𝐶 = 𝐷
Assertion
Ref Expression
psseq12i (𝐴𝐶𝐵𝐷)

Proof of Theorem psseq12i
StepHypRef Expression
1 psseq1i.1 . . 3 𝐴 = 𝐵
21psseq1i 3921 . 2 (𝐴𝐶𝐵𝐶)
3 psseq12i.2 . . 3 𝐶 = 𝐷
43psseq2i 3922 . 2 (𝐵𝐶𝐵𝐷)
52, 4bitri 267 1 (𝐴𝐶𝐵𝐷)
Colors of variables: wff setvar class
Syntax hints:  wb 198   = wceq 1658  wpss 3798
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-9 2175  ax-10 2194  ax-11 2209  ax-12 2222  ax-ext 2802
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 881  df-tru 1662  df-ex 1881  df-nf 1885  df-sb 2070  df-clab 2811  df-cleq 2817  df-clel 2820  df-ne 2999  df-in 3804  df-ss 3811  df-pss 3813
This theorem is referenced by: (None)
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