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Theorem pm2.27 39
Description: This theorem, called "Assertion," can be thought of as closed form of modus ponens ax-mp 7. Theorem *2.27 of [WhiteheadRussell] p. 104. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
pm2.27  |-  ( ph  ->  ( ( ph  ->  ps )  ->  ps )
)

Proof of Theorem pm2.27
StepHypRef Expression
1 id 19 . 2  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ps )
)
21com12 30 1  |-  ( ph  ->  ( ( ph  ->  ps )  ->  ps )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  pm2.43  52  com23  77  biimt  239  pm3.35  339  pm3.2im  599  mth8  612  pm2.65  618  condc  783  annimim  816  pm2.26dc  847  ax10o  1644  issref  4737  acexmidlem2  5540  findcard2  6423  findcard2s  6424  bj-inf2vnlem1  10923  bj-findis  10932
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