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Theorem axmp 193
Description: Rule of Modus Ponens. The postulated inference rule of propositional calculus. See e.g. Rule 1 of [Hamilton] p. 73.
Hypotheses
Ref Expression
axmp.1 |- S:*
axmp.2 |- T. |= R
axmp.3 |- T. |= [R ==> S]
Assertion
Ref Expression
axmp |- T. |= S
Proof of Theorem axmp
StepHypRef Expression
1 axmp.1 . 2 |- S:*
2 axmp.2 . 2 |- T. |= R
3 axmp.3 . 2 |- T. |= [R ==> S]
41, 2, 3mpd 146 1 |- T. |= S
Colors of variables: type var term
Syntax hints:  *hb 3  T.kt 8  [kbr 9   |= wffMMJ2 11  wffMMJ2t 12   ==> tim 111
This theorem was proved from axioms:  ax-syl 15  ax-jca 17  ax-simpl 20  ax-simpr 21  ax-id 24  ax-trud 26  ax-cb1 29  ax-cb2 30  ax-refl 39  ax-eqmp 42  ax-ded 43  ax-ceq 46  ax-beta 60  ax-distrc 61  ax-leq 62  ax-distrl 63  ax-hbl1 93  ax-17 95  ax-inst 103
This theorem depends on definitions:  df-ov 65  df-an 118  df-im 119
This theorem is referenced by: (None)
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