Theorem mt2i 110

Description: Modus tollens inference. (Contributed by NM, 26-Mar-1995.) (Proof shortened by Wolf Lammen, 15-Sep-2012.)

Hypotheses

Ref	Expression
mt2i.1	|- ch
mt2i.2	|- (ph -> (ps -> -. ch))

Assertion

Ref	Expression
mt2i	|- (ph -> -. ps)

Proof of Theorem mt2i

Step	Hyp	Ref	Expression
1		mt2i.1	. . 3 |- ch
2	1	a1i 10	. 2 |- (ph -> ch)
3		mt2i.2	. 2 |- (ph -> (ps -> -. ch))
4	2, 3	mt2d 109	1 |- (ph -> -. ps)

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: (None)