Theorem pm2.65i 165

Description: Inference rule for proof by contradiction. (Contributed by NM, 18-May-1994.) (Proof shortened by Wolf Lammen, 11-Sep-2013.)

Hypotheses

Ref	Expression
pm2.65i.1	|- (ph -> ps)
pm2.65i.2	|- (ph -> -. ps)

Assertion

Ref	Expression
pm2.65i	|- -. ph

Proof of Theorem pm2.65i

Step	Hyp	Ref	Expression
1		pm2.65i.2	. . 3 |- (ph -> -. ps)
2	1	con2i 112	. 2 |- (ps -> -. ph)
3		pm2.65i.1	. . 3 |- (ph -> ps)
4	3	con3i 127	. 2 |- (-. ps -> -. ph)
5	2, 4	pm2.61i 156	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:  mto  167  mt2  170  noel  3555