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Theorem sbf 2026
Description: Substitution for a variable not free in a wff does not affect it. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 4-Oct-2016.)
Hypothesis
Ref Expression
sbf.1 xφ
Assertion
Ref Expression
sbf ([y / x]φφ)

Proof of Theorem sbf
StepHypRef Expression
1 sbf.1 . 2 xφ
2 sbft 2025 . 2 (Ⅎxφ → ([y / x]φφ))
31, 2ax-mp 5 1 ([y / x]φφ)
Colors of variables: wff setvar class
Syntax hints:  wb 176  wnf 1544  [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:  sbh  2027  sbf2  2028  sb6x  2029  nfs1f  2030  sbequ5  2031  sbequ6  2032  sbt  2033  sbrim  2067  sblim  2068  sbrbif  2074  sbid2  2084  sbabel  2515
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