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Theorem oprabbidv 5564
 Description: Equivalent wff's yield equal operation class abstractions (deduction rule). (Contributed by NM, 21-Feb-2004.)
Hypothesis
Ref Expression
oprabbidv.1 (φ → (ψχ))
Assertion
Ref Expression
oprabbidv (φ → {x, y, z ψ} = {x, y, z χ})
Distinct variable groups:   x,z,φ   y,z,φ
Allowed substitution hints:   ψ(x,y,z)   χ(x,y,z)

Proof of Theorem oprabbidv
StepHypRef Expression
1 nfv 1619 . 2 xφ
2 nfv 1619 . 2 yφ
3 nfv 1619 . 2 zφ
4 oprabbidv.1 . 2 (φ → (ψχ))
51, 2, 3, 4oprabbid 5563 1 (φ → {x, y, z ψ} = {x, y, z χ})
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   = wceq 1642  {coprab 5527 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-oprab 5528 This theorem is referenced by:  oprabbii  5565  resoprab2  5582  mpt2eq123dv  5663  mpt2eq3dva  5669
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