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Theorem abeq2d 2462
 Description: Equality of a class variable and a class abstraction (deduction). (Contributed by NM, 16-Nov-1995.)
Hypothesis
Ref Expression
abeqd.1 (φA = {x ψ})
Assertion
Ref Expression
abeq2d (φ → (x Aψ))

Proof of Theorem abeq2d
StepHypRef Expression
1 abeqd.1 . . 3 (φA = {x ψ})
21eleq2d 2420 . 2 (φ → (x Ax {x ψ}))
3 abid 2341 . 2 (x {x ψ} ↔ ψ)
42, 3syl6bb 252 1 (φ → (x Aψ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   = wceq 1642   ∈ wcel 1710  {cab 2339 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-11 1746  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349 This theorem is referenced by:  fvelimab  5370
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