Theorem 2a1i 27

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 9	. 2 ⊢ (𝜑 → 𝜒)
3	2	a1d 22	1 ⊢ (𝜑 → (𝜓 → 𝜒))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  equvini  1746  sbcrext  3028  map1  6778  seq3id2  10444  fsum2d  11376  fsumabs  11406  fsumiun  11418  fprod2d  11564  cncfmptc  13222