Theorem dedt

Description: The weak deduction theorem. For more information, see the Weak Deduction Theorem page mmdeduction.html . (Contributed by NM, 26-Jun-2002) Revised to use the conditional operator. (Revised by BJ, 30-Sep-2019) Commute consequent. (Revised by Steven Nguyen, 27-Apr-2023)

	Ref	Expression
Hypotheses	dedt.1	|- ( ( if- ( ch , ph , ps ) <-> ph ) -> ( ta <-> th ) )
	dedt.2	|- ta
Assertion	dedt	|- ( ch -> th )

Proof

Step	Hyp	Ref	Expression
1		dedt.1	|- ( ( if- ( ch , ph , ps ) <-> ph ) -> ( ta <-> th ) )
2		dedt.2	|- ta
3		ifptru	|- ( ch -> ( if- ( ch , ph , ps ) <-> ph ) )
4	2 1	mpbii	|- ( ( if- ( ch , ph , ps ) <-> ph ) -> th )
5	3 4	syl	|- ( ch -> th )