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Theorem psseq12i 3381
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 3379 . 2  |-  ( A 
C.  C  <->  B  C.  C )
3 psseq12i.2 . . 3  |-  C  =  D
43psseq2i 3380 . 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 1649    C. wpss 3264
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2374  df-cleq 2380  df-clel 2383  df-ne 2552  df-in 3270  df-ss 3277  df-pss 3279
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