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Theorem dfrab2 3774
Description: Alternate definition of restricted class abstraction. (Contributed by NM, 20-Sep-2003.) (Proof shortened by BJ, 22-Apr-2019.)
Assertion
Ref Expression
dfrab2  |-  { x  e.  A  |  ph }  =  ( { x  |  ph }  i^i  A
)
Distinct variable group:    x, A
Allowed substitution hint:    ph( x)

Proof of Theorem dfrab2
StepHypRef Expression
1 dfrab3 3773 . 2  |-  { x  e.  A  |  ph }  =  ( A  i^i  { x  |  ph }
)
2 incom 3691 . 2  |-  ( A  i^i  { x  | 
ph } )  =  ( { x  | 
ph }  i^i  A
)
31, 2eqtri 2496 1  |-  { x  e.  A  |  ph }  =  ( { x  |  ph }  i^i  A
)
Colors of variables: wff setvar class
Syntax hints:    = wceq 1379   {cab 2452   {crab 2818    i^i cin 3475
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-or 370  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-nfc 2617  df-rab 2823  df-v 3115  df-in 3483
This theorem is referenced by:  dfsup2OLD  7903  lubdm  15466  glbdm  15479  psrbagsn  17959  ismbl  21700  eulerpartgbij  27979  orvcval4  28067  dfpred3  28859  fvline2  29401  nznngen  30849
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