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Theorem psseq2d 3442
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 3437 . 2  |-  ( A  =  B  ->  ( C  C.  A  <->  C  C.  B ) )
31, 2syl 16 1  |-  ( ph  ->  ( C  C.  A  <->  C 
C.  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 178    = wceq 1653    C. wpss 3323
This theorem is referenced by:  psseq12d  3443  php3  7295  inf3lem5  7589  infeq5i  7593  ackbij1lem15  8116  fin4en1  8191  chpsscon1  23008  chnle  23018  atcvatlem  23890  atcvati  23891  lsatcvat  29910
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-ne 2603  df-in 3329  df-ss 3336  df-pss 3338
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