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Theorem psseq12i 3360
 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 3358 . 2 (ACBC)
3 psseq12i.2 . . 3 C = D
43psseq2i 3359 . 2 (BCBD)
52, 4bitri 240 1 (ACBD)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176   = wceq 1642   ⊊ wpss 3258 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-pss 3261 This theorem is referenced by: (None)
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