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Theorem elrab3 2995
 Description: Membership in a restricted class abstraction, using implicit substitution. (Contributed by NM, 5-Oct-2006.)
Hypothesis
Ref Expression
elrab.1 (x = A → (φψ))
Assertion
Ref Expression
elrab3 (A B → (A {x B φ} ↔ ψ))
Distinct variable groups:   ψ,x   x,A   x,B
Allowed substitution hint:   φ(x)

Proof of Theorem elrab3
StepHypRef Expression
1 elrab.1 . . 3 (x = A → (φψ))
21elrab 2994 . 2 (A {x B φ} ↔ (A B ψ))
32baib 871 1 (A B → (A {x B φ} ↔ ψ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   = wceq 1642   ∈ wcel 1710  {crab 2618 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-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rab 2623  df-v 2861 This theorem is referenced by:  unimax  3925
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