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Theorem csbnest1gOLD 3189
 Description: Nest the composition of two substitutions. Obsolete as of 11-Nov-2016. (Contributed by NM, 23-May-2006.) (New usage is discouraged.)
Assertion
Ref Expression
csbnest1gOLD ((A V x B W) → [A / x][B / x]C = [[A / x]B / x]C)
Distinct variable group:   x,A
Allowed substitution hints:   B(x)   C(x)   V(x)   W(x)

Proof of Theorem csbnest1gOLD
StepHypRef Expression
1 csbnest1g 3188 . 2 (A V[A / x][B / x]C = [[A / x]B / x]C)
21adantr 451 1 ((A V x B W) → [A / x][B / x]C = [[A / x]B / x]C)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358  ∀wal 1540   = wceq 1642   ∈ wcel 1710  [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-3an 936  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  df-csb 3137 This theorem is referenced by: (None)
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