Theorem gm-sbtru

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

	Ref	Expression
Hypothesis	gm-sbtru.1	⊢ 𝐴 ∈ V
Assertion	gm-sbtru	⊢ ( [ 𝐴 / 𝑥 ] ⊤ ↔ ⊤ )

Proof

Step	Hyp	Ref	Expression
1		gm-sbtru.1	⊢ 𝐴 ∈ V
2		sbcg	⊢ ( 𝐴 ∈ V → ( [ 𝐴 / 𝑥 ] ⊤ ↔ ⊤ ) )
3	1 2	ax-mp	⊢ ( [ 𝐴 / 𝑥 ] ⊤ ↔ ⊤ )