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	$$⊢\phi \to \chi$$
	mpidan.2	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\to \theta$$
Assertion	mpidan	$$⊢\left(\phi \wedge \psi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		mpidan.1	$$⊢\phi \to \chi$$
2		mpidan.2	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\to \theta$$
3	1	adantr	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
4	3 2	mpdan	$$⊢\left(\phi \wedge \psi \right)\to \theta$$