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Theorem rspsbca 3125
 Description: Restricted quantifier version of Axiom 4 of [Mendelson] p. 69. (Contributed by NM, 14-Dec-2005.)
Assertion
Ref Expression
rspsbca ((A B x B φ) → [̣A / xφ)
Distinct variable group:   x,B
Allowed substitution hints:   φ(x)   A(x)

Proof of Theorem rspsbca
StepHypRef Expression
1 rspsbc 3124 . 2 (A B → (x B φ → [̣A / xφ))
21imp 418 1 ((A B x B φ) → [̣A / xφ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358   ∈ wcel 1710  ∀wral 2614  [̣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-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  df-sbc 3047 This theorem is referenced by: (None)
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