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Theorem imim12i 56
Description: Inference joining two implications. Inference associated with imim12 97. Its associated inference is 3syl 20. (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 30 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  57  dedlem0b  952  meredith  1491  pssnn  7691  kmlem1  8480  brdom5  8857  brdom4  8858  axpowndlem2  8923  xrge0infss  27903  naim1  30600  naim2  30601  meran1  30626  bj-gl4  30731  rp-fakeanorass  35568  fiinfi  35588  axc11next  36125
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