Theorem mt2i 125

Description: Modus tollens inference.

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	. 2 |- ch
2		mt2i.2	. . 3 |- (ph -> (ps -> -. ch))
3	2	con2d 107	. 2 |- (ph -> (ch -> -. ps))
4	1, 3	mpi 55	1 |- (ph -> -. ps)

Syntax hints:  -. wn 2   -> wi 3

This theorem is referenced by:  ssnlim 3970  elirrv 5700  discrlem3 7908  sqrlem18 7940  reconnlem4 15449  reconnlem5 15450  ipo0 16426  ifr0 16427

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

Copyright terms: Public domain