Theorem con4i 122

Description: Inference rule derived from axiom ax-3 8. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 21-Jun-2013.)

Hypothesis

Ref	Expression
con4i.1	⊢ (¬ φ → ¬ ψ)

Assertion

Ref	Expression
con4i	⊢ (ψ → φ)

Proof of Theorem con4i

Step	Hyp	Ref	Expression
1		notnot1 114	. 2 ⊢ (ψ → ¬ ¬ ψ)
2		con4i.1	. 2 ⊢ (¬ φ → ¬ ψ)
3	1, 2	nsyl2 119	1 ⊢ (ψ → φ)

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:  pm2.21i  123  mt4  129  modal-b  1752  ax10lem2  1937  ax9from9o  2148  ax67to7  2168  ax467to7  2172  necon2ai  2561  ndmfvrcl  5350  oprssdm  5612  ndmovrcl  5616