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Theorem psseq2d 3602
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
psseq2d  |-  ( ph  ->  ( C  C.  A  <->  C 
C.  B ) )

Proof of Theorem psseq2d
StepHypRef Expression
1 psseq1d.1 . 2  |-  ( ph  ->  A  =  B )
2 psseq2 3597 . 2  |-  ( A  =  B  ->  ( C  C.  A  <->  C  C.  B
) )
31, 2syl 16 1  |-  ( ph  ->  ( C  C.  A  <->  C 
C.  B ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184    = wceq 1379    C. wpss 3482
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-ne 2664  df-in 3488  df-ss 3495  df-pss 3497
This theorem is referenced by:  psseq12d  3603  php3  7715  inf3lem5  8061  infeq5i  8065  ackbij1lem15  8626  fin4en1  8701  chpsscon1  26245  chnle  26255  atcvatlem  27127  atcvati  27128  lsatcvat  34248
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