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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 ) )