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Theorem psseq2d 3269
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 3264 . 2  |-  ( A  =  B  ->  ( C  C.  A  <->  C  C.  B ) )
31, 2syl 15 1  |-  ( ph  ->  ( C  C.  A  <->  C 
C.  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    = wceq 1623    C. wpss 3153
This theorem is referenced by:  psseq12d  3270  php3  7047  inf3lem5  7333  infeq5i  7337  ackbij1lem15  7860  fin4en1  7935  chpsscon1  22083  chnle  22093  atcvatlem  22965  atcvati  22966  lsatcvatlem  29239  lsatcvat  29240
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-ne 2448  df-in 3159  df-ss 3166  df-pss 3168
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