Theorem mt2i 97

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 83	. 2 |- (ph -> (ch -> -. ps))
4	1, 3	mpi 44	1 |- (ph -> -. ps)

Syntax hints:  -. wn 1   -> wi 2

This theorem is referenced by:  ssnlim 2407  eirrv 3449  discrlem3 4715  sqrlem18 4748

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

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