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Theorem sbc6 3072
 Description: An equivalence for class substitution. (Contributed by NM, 23-Aug-1993.) (Proof shortened by Eric Schmidt, 17-Jan-2007.)
Hypothesis
Ref Expression
sbc6.1 A V
Assertion
Ref Expression
sbc6 ([̣A / xφx(x = Aφ))
Distinct variable group:   x,A
Allowed substitution hint:   φ(x)

Proof of Theorem sbc6
StepHypRef Expression
1 sbc6.1 . 2 A V
2 sbc6g 3071 . 2 (A V → ([̣A / xφx(x = Aφ)))
31, 2ax-mp 5 1 ([̣A / xφx(x = Aφ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∀wal 1540   = wceq 1642   ∈ wcel 1710  Vcvv 2859  [̣wsbc 3046 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-v 2861  df-sbc 3047 This theorem is referenced by:  intab  3956
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