Theorem mt3d 114

Description: Modus tollens deduction.

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 93	. 2 |- (ph -> (-. ch -> ps))
4	1, 3	mpd 26	1 |- (ph -> ps)

Syntax hints:  -. wn 2   -> wi 3

This theorem is referenced by:  ecase23d 920  nnsuc 3143  sdomdomtr 4455  zbtwnre 6177

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

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