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Theorem psseq1d 3383
Description: An equality deduction for the proper subclass relationship. (Contributed by NM, 9-Jun-2004.)
Hypothesis
Ref Expression
psseq1d.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
psseq1d  |-  ( ph  ->  ( A  C.  C  <->  B 
C.  C ) )

Proof of Theorem psseq1d
StepHypRef Expression
1 psseq1d.1 . 2  |-  ( ph  ->  A  =  B )
2 psseq1 3378 . 2  |-  ( A  =  B  ->  ( A  C.  C  <->  B  C.  C ) )
31, 2syl 16 1  |-  ( ph  ->  ( A  C.  C  <->  B 
C.  C ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177    = wceq 1649    C. wpss 3265
This theorem is referenced by:  psseq12d  3385  fin23lem32  8158  fin23lem35  8161  compssiso  8188  mrieqv2d  13792  mrissmrcd  13793  pgpfac1lem5  15565  islbs3  16155  chpsscon2  22856
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 2369
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 2375  df-cleq 2381  df-clel 2384  df-ne 2553  df-in 3271  df-ss 3278  df-pss 3280
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