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Theorem psseq2i 3353
Description: An equality inference for the proper subclass relationship. (Contributed by NM, 9-Jun-2004.)
Hypothesis
Ref Expression
psseq1i.1  |-  A  =  B
Assertion
Ref Expression
psseq2i  |-  ( C 
C.  A  <->  C  C.  B )

Proof of Theorem psseq2i
StepHypRef Expression
1 psseq1i.1 . 2  |-  A  =  B
2 psseq2 3351 . 2  |-  ( A  =  B  ->  ( C  C.  A  <->  C  C.  B ) )
31, 2ax-mp 8 1  |-  ( C 
C.  A  <->  C  C.  B )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    = wceq 1647    C. wpss 3239
This theorem is referenced by:  psseq12i  3354  disjpss  3593  infeq5i  7484
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1551  ax-5 1562  ax-17 1621  ax-9 1659  ax-8 1680  ax-6 1734  ax-7 1739  ax-11 1751  ax-12 1937  ax-ext 2347
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1324  df-ex 1547  df-nf 1550  df-sb 1654  df-clab 2353  df-cleq 2359  df-clel 2362  df-ne 2531  df-in 3245  df-ss 3252  df-pss 3254
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