Theorem sbtd

Description: A true statement is true upon substitution (deduction). A similar proof is possible for icht . (Contributed by SN, 4-May-2024)

	Ref	Expression
Hypothesis	sbtd.1	⊢ ( 𝜑 → 𝜓 )
Assertion	sbtd	⊢ ( 𝜑 → [ 𝑡 / 𝑥 ] 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		sbtd.1	⊢ ( 𝜑 → 𝜓 )
2	1	alrimiv	⊢ ( 𝜑 → ∀ 𝑥 𝜓 )
3		stdpc4	⊢ ( ∀ 𝑥 𝜓 → [ 𝑡 / 𝑥 ] 𝜓 )
4	2 3	syl	⊢ ( 𝜑 → [ 𝑡 / 𝑥 ] 𝜓 )