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Theorem imim12i 62
Description: Inference joining two implications. Inference associated with imim12 105. 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 (𝜑𝜓)
imim12i.2 (𝜒𝜃)
Assertion
Ref Expression
imim12i ((𝜓𝜒) → (𝜑𝜃))

Proof of Theorem imim12i
StepHypRef Expression
1 imim12i.1 . 2 (𝜑𝜓)
2 imim12i.2 . . 3 (𝜒𝜃)
32imim2i 16 . 2 ((𝜓𝜒) → (𝜓𝜃))
41, 3syl5 34 1 ((𝜓𝜒) → (𝜑𝜃))
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  63  dedlem0b  1042  meredith  1644  sbequ2  2241  sbequ2OLD  2242  pssnn  8951  pssnnOLD  9040  kmlem1  9906  brdom5  10285  brdom4  10286  axpowndlem2  10354  naim1  34578  naim2  34579  meran1  34600  bj-gl4  34777  bj-wnf1  34899  rp-fakeanorass  41120  fiinfi  41180  axc11next  42024
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