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Theorem psseq12i 3035
 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 3033 . 2 (𝐴𝐶𝐵𝐶)
3 psseq12i.2 . . 3 𝐶 = 𝐷
43psseq2i 3034 . 2 (𝐵𝐶𝐵𝐷)
52, 4bitri 173 1 (𝐴𝐶𝐵𝐷)
 Colors of variables: wff set class Syntax hints:   ↔ wb 98   = wceq 1243   ⊊ wpss 2918 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-ne 2206  df-in 2924  df-ss 2931  df-pss 2933 This theorem is referenced by: (None)
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