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Metamath Proof Explorer

Theorem embantd

Description: Deduction embedding an antecedent. (Contributed by Wolf Lammen, 4-Oct-2013)

Ref Expression
Hypotheses embantd.1 ⊢ φ → ψ
embantd.2 ⊢ φ → χ → θ
Assertion embantd ⊢ φ → ψ → χ → θ

Proof

Step Hyp Ref Expression
1 embantd.1 ⊢ φ → ψ
2 embantd.2 ⊢ φ → χ → θ
3 2 imim2d ⊢ φ → ψ → χ → ψ → θ
4 1 3 mpid ⊢ φ → ψ → χ → θ