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Theorem sbcthdv 3061
 Description: Deduction version of sbcth 3060. (Contributed by NM, 30-Nov-2005.) (Proof shortened by Andrew Salmon, 8-Jun-2011.)
Hypothesis
Ref Expression
sbcthdv.1 (φψ)
Assertion
Ref Expression
sbcthdv ((φ A V) → [̣A / xψ)
Distinct variable group:   φ,x
Allowed substitution hints:   ψ(x)   A(x)   V(x)

Proof of Theorem sbcthdv
StepHypRef Expression
1 sbcthdv.1 . . 3 (φψ)
21alrimiv 1631 . 2 (φxψ)
3 spsbc 3058 . 2 (A V → (xψ → [̣A / xψ))
42, 3mpan9 455 1 ((φ A V) → [̣A / xψ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358  ∀wal 1540   ∈ wcel 1710  [̣wsbc 3046 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-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-v 2861  df-sbc 3047 This theorem is referenced by: (None)
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