Theorem sbfal 38607

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 3817	. 2 ⊢ (𝐴 ∈ V → ([𝐴 / 𝑥]⊥ ↔ ⊥))
3	1, 2	ax-mp 5	1 ⊢ ([𝐴 / 𝑥]⊥ ↔ ⊥)

Syntax hints:   ↔ wb 208  ⊥wfal 1573   ∈ wcel 2143  Vcvv 3455  [wsbc 3745

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1816  ax-4 1830  ax-5 1931  ax-6 1988  ax-7 2029  ax-8 2145

This theorem depends on definitions:  df-bi 209  df-an 400  df-ex 1801  df-sb 2092  df-clab 2742  df-clel 2838  df-sbc 3746

This theorem is referenced by: (None)