Theorem a1d

Description: Deduction introducing an embedded antecedent. Deduction form of ax-1 and a1i . (Contributed by NM, 5-Jan-1993) (Proof shortened by Stefan Allan, 20-Mar-2006)

	Ref	Expression
Hypothesis	a1d.1	$$⊢\phi \to \psi$$
Assertion	a1d	$$⊢\phi \to \left(\chi \to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		a1d.1	$$⊢\phi \to \psi$$
2		ax-1	$$⊢\psi \to \left(\chi \to \psi \right)$$
3	1 2	syl	$$⊢\phi \to \left(\chi \to \psi \right)$$