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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