Theorem con3rr3 155

Description: Rotate through consequent right. (Contributed by Wolf Lammen, 3-Nov-2013.)

Hypothesis

Ref	Expression
con3rr3.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
con3rr3	⊢ (¬ 𝜒 → (𝜑 → ¬ 𝜓))

Proof of Theorem con3rr3

Step	Hyp	Ref	Expression
1		con3rr3.1	. . 3 ⊢ (𝜑 → (𝜓 → 𝜒))
2	1	con3d 152	. 2 ⊢ (𝜑 → (¬ 𝜒 → ¬ 𝜓))
3	2	com12 32	1 ⊢ (¬ 𝜒 → (𝜑 → ¬ 𝜓))

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by:  impi  164  dfbi1  213  ax13b  2034  mo2icl  3661  otsndisj  5465  uzwo  12850  ssnn0fi  13936  wrdnfi  14499  s3sndisj  14918  hmeofval  23732  alexsubALTlem4  24024  nbuhgr  29431  nb3grprlem2  29469  vtxdginducedm1lem4  29631  iswwlksnon  29941  clwwlkn  30116  clwwlknon  30180  cvnbtwn  32377  bj-fvimacnv0  37613  not12an2impnot1  45010