Theorem pm2.24i 151

Description: Inference associated with pm2.24 125. Its associated inference is pm2.24ii 121. (Contributed by NM, 20-Aug-2001.)

Hypothesis

Ref	Expression
pm2.24i.1	⊢ 𝜑

Assertion

Ref	Expression
pm2.24i	⊢ (¬ 𝜑 → 𝜓)

Proof of Theorem pm2.24i

Step	Hyp	Ref	Expression
1		pm2.24i.1	. . 3 ⊢ 𝜑
2	1	a1i 11	. 2 ⊢ (¬ 𝜓 → 𝜑)
3	2	con1i 148	1 ⊢ (¬ 𝜑 → 𝜓)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is used by:  orci  879  niabn  1038  ax13dgen1  2174  snopeqop  5483  prm23ge5  16907  pmtrdifellem4  19606  2irrexpq  26968  usgredg2v  29687  frgr3vlem1  30753  frgr3vlem2  30754  3vfriswmgrlem  30757  negsym1  37036  wl-moteq  38277  nnn1suc  43147  euoreqb  47997  line2ylem  49681