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Theorem psseq2i 3401
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 3399 . 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 177    = wceq 1649    C. wpss 3285
This theorem is referenced by:  psseq12i  3402  disjpss  3642  infeq5i  7551
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 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2389
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 2395  df-cleq 2401  df-clel 2404  df-ne 2573  df-in 3291  df-ss 3298  df-pss 3300
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