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Theorem sbcgfi 3864
Description: Substitution for a variable not free in a wff does not affect it, in inference form. (Contributed by Giovanni Mascellani, 1-Jun-2019.)
Hypotheses
Ref Expression
sbcgfi.1 𝐴 ∈ V
sbcgfi.2 𝑥𝜑
Assertion
Ref Expression
sbcgfi ([𝐴 / 𝑥]𝜑𝜑)

Proof of Theorem sbcgfi
StepHypRef Expression
1 sbcgfi.1 . 2 𝐴 ∈ V
2 sbcgfi.2 . . 3 𝑥𝜑
32sbcgf 3861 . 2 (𝐴 ∈ V → ([𝐴 / 𝑥]𝜑𝜑))
41, 3ax-mp 5 1 ([𝐴 / 𝑥]𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 206  wnf 1783  wcel 2108  Vcvv 3480  [wsbc 3788
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-12 2177  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-nf 1784  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-sbc 3789
This theorem is referenced by:  csbgfi  3919  bnj110  34872  bnj1039  34985  mptsnunlem  37339  sbali  38119  sbexi  38120
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