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Theorem hbsb2 2057
 Description: Bound-variable hypothesis builder for substitution. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
hbsb2 x x = y → ([y / x]φx[y / x]φ))

Proof of Theorem hbsb2
StepHypRef Expression
1 sb4 2053 . 2 x x = y → ([y / x]φx(x = yφ)))
2 sb2 2023 . . 3 (x(x = yφ) → [y / x]φ)
32a5i 1789 . 2 (x(x = yφ) → x[y / x]φ)
41, 3syl6 29 1 x x = y → ([y / x]φx[y / x]φ))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1540  [wsb 1648 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 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649 This theorem is referenced by:  nfsb2  2058  sbequi  2059  sb9i  2094  hbs1  2105
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