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 ) )