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Theorem dfima4 4952
 Description: Alternate definition of image. Compare definition (d) of [Enderton] p. 44. (The proof was shortened by Andrew Salmon, 27-Aug-2011.) (Contributed by set.mm contributors, 14-Aug-1994.) (Revised by set.mm contributors, 27-Aug-2011.)
Assertion
Ref Expression
dfima4 (AB) = {y x(x B x, y A)}
Distinct variable groups:   x,y,A   x,B,y

Proof of Theorem dfima4
StepHypRef Expression
1 df-ima 4727 . 2 (AB) = {y x B xAy}
2 df-br 4640 . . . . 5 (xAyx, y A)
32rexbii 2639 . . . 4 (x B xAyx B x, y A)
4 df-rex 2620 . . . 4 (x B x, y Ax(x B x, y A))
53, 4bitri 240 . . 3 (x B xAyx(x B x, y A))
65abbii 2465 . 2 {y x B xAy} = {y x(x B x, y A)}
71, 6eqtri 2373 1 (AB) = {y x(x B x, y A)}
 Colors of variables: wff setvar class Syntax hints:   ∧ wa 358  ∃wex 1541   = wceq 1642   ∈ wcel 1710  {cab 2339  ∃wrex 2615  ⟨cop 4561   class class class wbr 4639   “ cima 4722 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-rex 2620  df-br 4640  df-ima 4727 This theorem is referenced by:  imassrn  5009  imai  5010
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