Theorem sbfal 39182

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 3814	. 2 ⊢ (𝐴 ∈ V → ([𝐴 / 𝑥]⊥ ↔ ⊥))
3	1, 2	ax-mp 5	1 ⊢ ([𝐴 / 𝑥]⊥ ↔ ⊥)

This proof depends on syntax axioms:   ↔ wb 209  ⊥wfal 1581   ∈ wcel 2146  Vcvv 3454  [wsbc 3742

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1944  ax-6 2001  ax-7 2042  ax-8 2148

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1812  df-sb 2101  df-clab 2742  df-clel 2839  df-sbc 3743

This theorem is used by: (None)