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	|- ( ph -> ps )
Assertion	sbtd	|- ( ph -> [ t / x ] ps )

Proof

Step	Hyp	Ref	Expression
1		sbtd.1	|- ( ph -> ps )
2	1	alrimiv	|- ( ph -> A. x ps )
3		stdpc4	|- ( A. x ps -> [ t / x ] ps )
4	2 3	syl	|- ( ph -> [ t / x ] ps )