Theorem 2a1i 24

Description: Add two antecedents to a wff. (Contributed by Jeff Hankins, 4-Aug-2009.) (Proof shortened by Wolf Lammen, 23-Jul-2013.)

Hypothesis

Ref	Expression
2a1i.1	⊢ χ

Assertion

Ref	Expression
2a1i	⊢ (φ → (ψ → χ))

Proof of Theorem 2a1i

Step	Hyp	Ref	Expression
1		2a1i.1	. . 3 ⊢ χ
2	1	a1i 10	. 2 ⊢ (φ → χ)
3	2	a1d 22	1 ⊢ (φ → (ψ → χ))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is used by:  ax12dgen3  1727  equvini  1987  ax11f  2192