Theorem con3rr3 128

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 125	. 2 ⊢ (φ → (¬ χ → ¬ ψ))
3	2	com12 27	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  140  ax12b  1689  equs5e  1888  ax12  1935  ax10lem2  1937  sbn  2062  ax12from12o  2156  mo2icl  3016