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Theorem mt3i 126
Description: Modus tollens inference. (Contributed by NM, 26-Mar-1995.) (Proof shortened by Wolf Lammen, 15-Sep-2012.)
Hypotheses
Ref Expression
mt3i.1  |-  -.  ch
mt3i.2  |-  ( ph  ->  ( -.  ps  ->  ch ) )
Assertion
Ref Expression
mt3i  |-  ( ph  ->  ps )

Proof of Theorem mt3i
StepHypRef Expression
1 mt3i.1 . . 3  |-  -.  ch
21a1i 11 . 2  |-  ( ph  ->  -.  ch )
3 mt3i.2 . 2  |-  ( ph  ->  ( -.  ps  ->  ch ) )
42, 3mt3d 125 1  |-  ( ph  ->  ps )
Colors of variables: wff setvar class
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:  ordeleqon  6623  wofib  7988  harcard  8376  infpssALT  8710  zorn2lem4  8896  lt6abl  17023  gzrngunitlem  18608  bwth  20036  i1f0rn  22214  dfon2lem3  29391
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