Theorem bj-alsyl

Description: Syllogism under the universal quantifier, in the curried form appearing as Theorem *10.3 of WhiteheadRussell p. 145. See alsyl for the uncurried form. (Contributed by BJ, 28-Mar-2026)

	Ref	Expression
Assertion	bj-alsyl	|- ( A. x ( ph -> ps ) -> ( A. x ( ps -> ch ) -> A. x ( ph -> ch ) ) )

Proof

Step	Hyp	Ref	Expression
1		imim1	|- ( ( ph -> ps ) -> ( ( ps -> ch ) -> ( ph -> ch ) ) )
2	1	al2imi	|- ( A. x ( ph -> ps ) -> ( A. x ( ps -> ch ) -> A. x ( ph -> ch ) ) )