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Theorem sbfal 35538
Description: Substitution does not change falsity. (Contributed by Giovanni Mascellani, 24-May-2019.)
Hypothesis
Ref Expression
sbfal.1 𝐴 ∈ V
Assertion
Ref Expression
sbfal ([𝐴 / 𝑥]⊥ ↔ ⊥)

Proof of Theorem sbfal
StepHypRef Expression
1 sbfal.1 . 2 𝐴 ∈ V
2 sbcg 3796 . 2 (𝐴 ∈ V → ([𝐴 / 𝑥]⊥ ↔ ⊥))
31, 2ax-mp 5 1 ([𝐴 / 𝑥]⊥ ↔ ⊥)
Colors of variables: wff setvar class
Syntax hints:  wb 209  wfal 1550  wcel 2112  Vcvv 3444  [wsbc 3723
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2114  ax-9 2122  ax-12 2176  ax-ext 2773
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2780  df-cleq 2794  df-clel 2873  df-sbc 3724
This theorem is referenced by: (None)
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