Theorem sbfal 33909

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 3503	. 2 ⊢ (𝐴 ∈ V → ([𝐴 / 𝑥]⊥ ↔ ⊥))
3	1, 2	ax-mp 5	1 ⊢ ([𝐴 / 𝑥]⊥ ↔ ⊥)

Syntax hints:   ↔ wb 196  ⊥wfal 1488   ∈ wcel 1990  Vcvv 3200  [wsbc 3435

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-v 3202  df-sbc 3436

This theorem is referenced by: (None)