Theorem a2i 11

Description: Inference derived from Axiom ax-2 7. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
a2i.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
a2i	⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜒))

Proof of Theorem a2i

Step	Hyp	Ref	Expression
1		a2i.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
2		ax-2 7	. 2 ⊢ ((𝜑 → (𝜓 → 𝜒)) → ((𝜑 → 𝜓) → (𝜑 → 𝜒)))
3	1, 2	ax-mp 5	1 ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜒))

Syntax hints:   → wi 4

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

This theorem is referenced by:  imim2i  12  mpd  13  sylcom  28  pm2.43  53  ancl  318  ancr  321  anc2r  328  pm2.65  659  pm2.18dc  855  con4biddc  857  hbim1  1570  sbcof2  1810  ralimia  2538  ceqsalg  2765  rspct  2834  elabgt  2878  fvmptt  5604  ordiso2  7029  bj-exlimmp  14292  bj-rspgt  14309  bj-indint  14454