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Theorem rspcsbela 3195
 Description: Special case related to rspsbc 3124. (Contributed by NM, 10-Dec-2005.) (Proof shortened by Eric Schmidt, 17-Jan-2007.)
Assertion
Ref Expression
rspcsbela ((A B x B C D) → [A / x]C D)
Distinct variable groups:   x,B   x,D
Allowed substitution hints:   A(x)   C(x)

Proof of Theorem rspcsbela
StepHypRef Expression
1 rspsbc 3124 . . 3 (A B → (x B C D → [̣A / xC D))
2 sbcel1g 3155 . . 3 (A B → ([̣A / xC D[A / x]C D))
31, 2sylibd 205 . 2 (A B → (x B C D[A / x]C D))
43imp 418 1 ((A B x B C D) → [A / x]C D)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358   ∈ wcel 1710  ∀wral 2614  [̣wsbc 3046  [csb 3136 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  df-csb 3137 This theorem is referenced by: (None)
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