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Theorem hbs1 2105
 Description: x is not free in [y / x]φ when x and y are distinct. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
hbs1 ([y / x]φx[y / x]φ)
Distinct variable group:   x,y
Allowed substitution hints:   φ(x,y)

Proof of Theorem hbs1
StepHypRef Expression
1 ax16 2045 . 2 (x x = y → ([y / x]φx[y / x]φ))
2 hbsb2 2057 . 2 x x = y → ([y / x]φx[y / x]φ))
31, 2pm2.61i 156 1 ([y / x]φx[y / x]φ)
 Colors of variables: wff setvar class Syntax hints:   → 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:  nfs1v  2106  hbab1  2342
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