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	$$⊢\phi \to \psi$$
Assertion	sbtd	$$⊢\phi \to \left[t/x\right]\psi$$

Proof

Step	Hyp	Ref	Expression
1		sbtd.1	$$⊢\phi \to \psi$$
2	1	alrimiv	$$⊢\phi \to \forall x\psi$$
3		stdpc4	$$⊢\forall x\psi \to \left[t/x\right]\psi$$
4	2 3	syl	$$⊢\phi \to \left[t/x\right]\psi$$