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Theorem psseq12i 3660
 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 3658 . 2 (𝐴𝐶𝐵𝐶)
3 psseq12i.2 . . 3 𝐶 = 𝐷
43psseq2i 3659 . 2 (𝐵𝐶𝐵𝐷)
52, 4bitri 263 1 (𝐴𝐶𝐵𝐷)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 195   = wceq 1475   ⊊ wpss 3541 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-ne 2782  df-in 3547  df-ss 3554  df-pss 3556 This theorem is referenced by: (None)
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