Theorem mt3 192

Description: A rule similar to modus tollens. Inference associated with con1i 144. (Contributed by NM, 18-May-1994.) (Proof shortened by Wolf Lammen, 11-Sep-2013.)

Hypotheses

Ref	Expression
mt3.1	|- -. ps
mt3.2	|- ( -. ph -> ps )

Assertion

Ref	Expression
mt3	|- ph

Proof of Theorem mt3

Step	Hyp	Ref	Expression
1		mt3.1	. . 3 |- -. ps
2		mt3.2	. . 3 |- ( -. ph -> ps )
3	1, 2	mto 188	. 2 |- -. -. ph
4	3	notnotri 126	1 |- ph

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:  wfrlem16  7430  sinhalfpilem  24215  equidq  34209  etransc  40500