Theorem mt3d 117

Description: Modus tollens deduction. (Contributed by NM, 26-Mar-1995.)

Hypotheses

Ref	Expression
mt3d.1	|- (ph -> -. ch)
mt3d.2	|- (ph -> (-. ps -> ch))

Assertion

Ref	Expression
mt3d	|- (ph -> ps)

Proof of Theorem mt3d

Step	Hyp	Ref	Expression
1		mt3d.1	. 2 |- (ph -> -. ch)
2		mt3d.2	. . 3 |- (ph -> (-. ps -> ch))
3	2	con1d 116	. 2 |- (ph -> (-. ch -> ps))
4	1, 3	mpd 14	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:  mt3i  118  nsyl2  119  ecase23d  1285  nnsucelr  4429  enprmaplem5  6081