Theorem mt3i 118

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

Hypotheses

Ref	Expression
mt3i.1	|- -. ch
mt3i.2	|- (ph -> (-. ps -> ch))

Assertion

Ref	Expression
mt3i	|- (ph -> ps)

Proof of Theorem mt3i

Step	Hyp	Ref	Expression
1		mt3i.1	. . 3 |- -. ch
2	1	a1i 10	. 2 |- (ph -> -. ch)
3		mt3i.2	. 2 |- (ph -> (-. ps -> ch))
4	2, 3	mt3d 117	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)