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Theorem vtoclri 2929
 Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 21-Nov-1994.)
Hypotheses
Ref Expression
vtoclri.1 (x = A → (φψ))
vtoclri.2 x B φ
Assertion
Ref Expression
vtoclri (A Bψ)
Distinct variable groups:   x,A   x,B   ψ,x
Allowed substitution hint:   φ(x)

Proof of Theorem vtoclri
StepHypRef Expression
1 vtoclri.1 . 2 (x = A → (φψ))
2 vtoclri.2 . . 3 x B φ
32rspec 2678 . 2 (x Bφ)
41, 3vtoclga 2920 1 (A Bψ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   = wceq 1642   ∈ wcel 1710  ∀wral 2614 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-ral 2619  df-v 2861 This theorem is referenced by: (None)
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