Theorem gm-sbtru

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

	Ref	Expression
Hypothesis	gm-sbtru.1	$$⊢A\in \mathrm{V}$$
Assertion	gm-sbtru	$$⊢\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\top \leftrightarrow \top$$

Proof

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