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Theorem hbs1f 1642
Description: If x is not free in φ, it is not free in [y / x]φ. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Hypothesis
Ref Expression
hbs1f.1 (φxφ)
Assertion
Ref Expression
hbs1f ([y / x]φx[y / x]φ)

Proof of Theorem hbs1f
StepHypRef Expression
1 hbs1f.1 . . 3 (φxφ)
21sbh 1637 . 2 ([y / x]φφ)
32, 1hbxfrbi 1337 1 ([y / x]φx[y / x]φ)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1224  [wsb 1623
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1312  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-4 1377  ax-i9 1400  ax-ial 1405
This theorem depends on definitions:  df-bi 110  df-sb 1624
This theorem is referenced by: (None)
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