Theorem sbfal

Description: Substitution does not change falsity. (Contributed by Giovanni Mascellani, 24-May-2019)

	Ref	Expression
Hypothesis	sbfal.1	$$⊢A\in \mathrm{V}$$
Assertion	sbfal	$$⊢\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\perp \leftrightarrow \perp$$

Proof

Step	Hyp	Ref	Expression
1		sbfal.1	$$⊢A\in \mathrm{V}$$
2		sbcg	$$⊢A\in \mathrm{V}\to \left(\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\perp \leftrightarrow \perp \right)$$
3	1 2	ax-mp	$$⊢\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\perp \leftrightarrow \perp$$