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Theorem imim12i 59
Description: Inference joining two implications. Inference associated with imim12 100. Its associated inference is 3syl 18. (Contributed by NM, 12-Mar-1993.) (Proof shortened by Mel L. O'Cat, 29-Oct-2011.)
Hypotheses
Ref Expression
imim12i.1  |-  ( ph  ->  ps )
imim12i.2  |-  ( ch 
->  th )
Assertion
Ref Expression
imim12i  |-  ( ( ps  ->  ch )  ->  ( ph  ->  th )
)

Proof of Theorem imim12i
StepHypRef Expression
1 imim12i.1 . 2  |-  ( ph  ->  ps )
2 imim12i.2 . . 3  |-  ( ch 
->  th )
32imim2i 16 . 2  |-  ( ( ps  ->  ch )  ->  ( ps  ->  th )
)
41, 3syl5 33 1  |-  ( ( ps  ->  ch )  ->  ( ph  ->  th )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  imim1i  60  dedlem0b  970  meredith  1534  pssnn  7815  kmlem1  8605  brdom5  8982  brdom4  8983  axpowndlem2  9048  xrge0infssOLD  28389  naim1  31093  naim2  31094  meran1  31119  bj-gl4  31223  rp-fakeanorass  36201  fiinfi  36221  axc11next  36800
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