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Theorem sbfal 32877
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 3464 . 2 (𝐴 ∈ V → ([𝐴 / 𝑥]⊥ ↔ ⊥))
31, 2ax-mp 5 1 ([𝐴 / 𝑥]⊥ ↔ ⊥)
Colors of variables: wff setvar class
Syntax hints:  wb 194  wfal 1479  wcel 1975  Vcvv 3167  [wsbc 3396
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1711  ax-4 1726  ax-5 1825  ax-6 1873  ax-7 1920  ax-12 2031  ax-13 2227  ax-ext 2584
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1866  df-clab 2591  df-cleq 2597  df-clel 2600  df-v 3169  df-sbc 3397
This theorem is referenced by: (None)
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