Theorem mt2i 644

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

Hypotheses

Ref	Expression
mt2i.1	|- ch
mt2i.2	|- ( ph -> ( ps -> -. ch ) )

Assertion

Ref	Expression
mt2i	|- ( ph -> -. ps )

Proof of Theorem mt2i

Step	Hyp	Ref	Expression
1		mt2i.1	. . 3 |- ch
2	1	a1i 9	. 2 |- ( ph -> ch )
3		mt2i.2	. 2 |- ( ph -> ( ps -> -. ch ) )
4	2, 3	mt2d 625	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-in1 614  ax-in2 615

This theorem is referenced by:  0mnnnnn0  9208  climuni  11301  ennnfonelemk  12401