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Theorem expdimp 250
Description: A deduction version of exportation, followed by importation. (Contributed by NM, 6-Sep-2008.)
Hypothesis
Ref Expression
exp3a.1 (𝜑 → ((𝜓𝜒) → 𝜃))
Assertion
Ref Expression
expdimp ((𝜑𝜓) → (𝜒𝜃))

Proof of Theorem expdimp
StepHypRef Expression
1 exp3a.1 . . 3 (𝜑 → ((𝜓𝜒) → 𝜃))
21expd 249 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
32imp 119 1 ((𝜑𝜓) → (𝜒𝜃))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem is referenced by:  rexlimdvv  2456  reu6  2753  fun11iun  5175  poxp  5881  smoel  5946  iinerm  6209  prarloclemlo  6650  peano5uzti  8405  lbzbi  8648  ssfzo12bi  9183  cau3lem  9941  alzdvds  10166  nno  10218  nn0seqcvgd  10263
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