Theorem mpidan

Description: A deduction which "stacks" a hypothesis. (Contributed by Stanislas Polu, 9-Mar-2020) (Proof shortened by Wolf Lammen, 28-Mar-2021)

	Ref	Expression
Hypotheses	mpidan.1	|- ( ph -> ch )
	mpidan.2	|- ( ( ( ph /\ ps ) /\ ch ) -> th )
Assertion	mpidan	|- ( ( ph /\ ps ) -> th )

Proof

Step	Hyp	Ref	Expression
1		mpidan.1	|- ( ph -> ch )
2		mpidan.2	|- ( ( ( ph /\ ps ) /\ ch ) -> th )
3	1	adantr	|- ( ( ph /\ ps ) -> ch )
4	3 2	mpdan	|- ( ( ph /\ ps ) -> th )