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Theorem rspccva 2954
 Description: Restricted specialization, using implicit substitution. (Contributed by NM, 26-Jul-2006.) (Proof shortened by Andrew Salmon, 8-Jun-2011.)
Hypothesis
Ref Expression
rspcv.1 (x = A → (φψ))
Assertion
Ref Expression
rspccva ((x B φ A B) → ψ)
Distinct variable groups:   x,A   x,B   ψ,x
Allowed substitution hint:   φ(x)

Proof of Theorem rspccva
StepHypRef Expression
1 rspcv.1 . . 3 (x = A → (φψ))
21rspcv 2951 . 2 (A B → (x B φψ))
32impcom 419 1 ((x B φ A B) → ψ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   ∧ wa 358   = wceq 1642   ∈ wcel 1710  ∀wral 2614 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-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:  disjne  3596  foelrn  5425  fconstfv  5456  nchoicelem17  6305
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