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Theorem sbh 2027
Description: Substitution for a variable not free in a wff does not affect it. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
sbh.1 (φxφ)
Assertion
Ref Expression
sbh ([y / x]φφ)

Proof of Theorem sbh
StepHypRef Expression
1 sbh.1 . . 3 (φxφ)
21nfi 1551 . 2 xφ
32sbf 2026 1 ([y / x]φφ)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176  wal 1540  [wsb 1648
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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: (None)
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