Theorem mt3i 113

Description: Modus tollens inference.

Hypotheses

Ref	Expression
mt3i.1	|- -. ch
mt3i.2	|- (ph -> (-. ps -> ch))

Assertion

Ref	Expression
mt3i	|- (ph -> ps)

Proof of Theorem mt3i

Step	Hyp	Ref	Expression
1		mt3i.1	. 2 |- -. ch
2		mt3i.2	. . 3 |- (ph -> (-. ps -> ch))
3	2	con1d 93	. 2 |- (ph -> (-. ch -> ps))
4	1, 3	mpi 44	1 |- (ph -> ps)

Syntax hints:  -. wn 2   -> wi 3

This theorem is referenced by:  a16g 1276  ordeleqon 2990  limom 3146  zorn2lem4 4791  crulem 6736

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

Copyright terms: Public domain