Theorem mt4i 131

Description: Modus tollens inference. (Contributed by Wolf Lammen, 12-May-2013.)

Hypotheses

Ref	Expression
mt4i.1	|- ch
mt4i.2	|- (ph -> (-. ps -> -. ch))

Assertion

Ref	Expression
mt4i	|- (ph -> ps)

Proof of Theorem mt4i

Step	Hyp	Ref	Expression
1		mt4i.1	. . 3 |- ch
2	1	a1i 10	. 2 |- (ph -> ch)
3		mt4i.2	. 2 |- (ph -> (-. ps -> -. ch))
4	2, 3	mt4d 130	1 |- (ph -> ps)

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: (None)