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Theorem opabbidv 4625
 Description: Equivalent wff's yield equal ordered-pair class abstractions (deduction rule). (Contributed by NM, 15-May-1995.)
Hypothesis
Ref Expression
opabbidv.1 (φ → (ψχ))
Assertion
Ref Expression
opabbidv (φ → {x, y ψ} = {x, y χ})
Distinct variable groups:   φ,x   φ,y
Allowed substitution hints:   ψ(x,y)   χ(x,y)

Proof of Theorem opabbidv
StepHypRef Expression
1 nfv 1619 . 2 xφ
2 nfv 1619 . 2 yφ
3 opabbidv.1 . 2 (φ → (ψχ))
41, 2, 3opabbid 4624 1 (φ → {x, y ψ} = {x, y χ})
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   = wceq 1642  {copab 4622 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-opab 4623 This theorem is referenced by:  opabbii  4626  csbopabg  4637  xpeq1  4798  xpeq2  4799  opabbi2dv  4867  resopab2  5001  cores  5084  f1oiso2  5500  f1od  5726
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