Theorem mt2d 634

Description: Modus tollens deduction. (Contributed by NM, 4-Jul-1994.)

Hypotheses

Ref	Expression
mt2d.1	|- ( ph -> ch )
mt2d.2	|- ( ph -> ( ps -> -. ch ) )

Assertion

Ref	Expression
mt2d	|- ( ph -> -. ps )

Proof of Theorem mt2d

Step	Hyp	Ref	Expression
1		mt2d.1	. 2 |- ( ph -> ch )
2		mt2d.2	. . 3 |- ( ph -> ( ps -> -. ch ) )
3	2	con2d 633	. 2 |- ( ph -> ( ch -> -. ps ) )
4	1, 3	mpd 13	1 |- ( ph -> -. ps )

This proof depends on syntax axioms:   -. wn 3   -> wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 623  ax-in2 624

This theorem is used by:  nsyl3  635  mt2i  653  en2lp  4701  recnz  9744  xnn0dcle  10215  fznuz  10520  uznfz  10521  nninfctlemfo  12836  pcadd  13142  ballotfilemfrcn0  13325  oddennn  13335  perfectlem1  16260  lgseisenlem1  16355