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Metamath Proof Explorer

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 )