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Theorem psseq12i 3430
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  |-  ( A 
C.  C  <->  B  C.  D )

Proof of Theorem psseq12i
StepHypRef Expression
1 psseq1i.1 . . 3  |-  A  =  B
21psseq1i 3428 . 2  |-  ( A 
C.  C  <->  B  C.  C )
3 psseq12i.2 . . 3  |-  C  =  D
43psseq2i 3429 . 2  |-  ( B 
C.  C  <->  B  C.  D )
52, 4bitri 241 1  |-  ( A 
C.  C  <->  B  C.  D )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    = wceq 1652    C. wpss 3313
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-ne 2600  df-in 3319  df-ss 3326  df-pss 3328
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