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))

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:  equvini  1811  sbcrext  3129  map1  7101  modom  7108  seq3id2  10965  pfxccatin12lem3  11506  fsum2d  12204  fsumabs  12234  fsumiun  12246  fprod2d  12392  cncfmptc  15699