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	⊢ ( 𝜑 → 𝜒 )
	mpidan.2	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )
Assertion	mpidan	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		mpidan.1	⊢ ( 𝜑 → 𝜒 )
2		mpidan.2	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )
3	1	adantr	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
4	3 2	mpdan	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜃 )