Theorem con3rr3 642

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 640	. 2 ⊢ (𝜑 → (¬ 𝜒 → ¬ 𝜓))
3	2	com12 30	1 ⊢ (¬ 𝜒 → (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-in1 623  ax-in2 624

This theorem is used by:  imnan  701  snnen2og  7160  bj-nnim  16763