Theorem sbfal 38680

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

Step	Hyp	Ref	Expression
1		sbfal.1	. 2 ⊢ 𝐴 ∈ V
2		sbcg 3825	. 2 ⊢ (𝐴 ∈ V → ([𝐴 / 𝑥]⊥ ↔ ⊥))
3	1, 2	ax-mp 5	1 ⊢ ([𝐴 / 𝑥]⊥ ↔ ⊥)

Syntax hints:   ↔ wb 209  ⊥wfal 1579   ∈ wcel 2149  Vcvv 3463  [wsbc 3753

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151

This theorem depends on definitions:  df-bi 210  df-an 401  df-ex 1807  df-sb 2098  df-clab 2748  df-clel 2844  df-sbc 3754

This theorem is referenced by: (None)