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Theorem psseq2d 3560
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 3555 . 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 1370    C. wpss 3440
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-ne 2650  df-in 3446  df-ss 3453  df-pss 3455
This theorem is referenced by:  psseq12d  3561  php3  7610  inf3lem5  7953  infeq5i  7957  ackbij1lem15  8518  fin4en1  8593  chpsscon1  25086  chnle  25096  atcvatlem  25968  atcvati  25969  lsatcvat  33058
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