Theorem mtoi 169

Description: Modus tollens inference. (Contributed by NM, 5-Jul-1994.) (Proof shortened by Wolf Lammen, 15-Sep-2012.)

Hypotheses

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

Assertion

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

Proof of Theorem mtoi

Step	Hyp	Ref	Expression
1		mtoi.1	. . 3 |- -. ch
2	1	a1i 10	. 2 |- (ph -> -. ch)
3		mtoi.2	. 2 |- (ph -> (ps -> ch))
4	2, 3	mtod 168	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:  mtbii  293  mtbiri  294  sp  1747  spOLD  1748  equsalhwOLD  1839  dvelimv  1939  ax9o  1950  nndisjeq  4429  sfinltfin  4535  vfin1cltv  4547  nulnnn  4556  nmembers1lem2  6269