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Theorem hbsb3 1686
Description: If y is not free in φ, x is not free in [y / x]φ. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
hbsb3.1 (φyφ)
Assertion
Ref Expression
hbsb3 ([y / x]φx[y / x]φ)

Proof of Theorem hbsb3
StepHypRef Expression
1 hbsb3.1 . . 3 (φyφ)
21sbimi 1644 . 2 ([y / x]φ → [y / x]yφ)
3 hbsb2a 1684 . 2 ([y / x]yφx[y / x]φ)
42, 3syl 14 1 ([y / x]φx[y / x]φ)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1240  [wsb 1642
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 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-11 1394  ax-4 1397  ax-i9 1420  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-sb 1643
This theorem is referenced by:  nfs1  1687  sbcof2  1688  ax16  1691  sb8h  1731  sb8eh  1732  ax16ALT  1736
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