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Theorem psseq12i 3280
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 3278 . 2  |-  ( A 
C.  C  <->  B  C.  C )
3 psseq12i.2 . . 3  |-  C  =  D
43psseq2i 3279 . 2  |-  ( B 
C.  C  <->  B  C.  D )
52, 4bitri 240 1  |-  ( A 
C.  C  <->  B  C.  D )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    = wceq 1632    C. wpss 3166
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-ne 2461  df-in 3172  df-ss 3179  df-pss 3181
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