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Theorem expdimp 246
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 245 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
32imp 115 1 ((𝜑𝜓) → (𝜒𝜃))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem is referenced by:  rexlimdvv  2439  reu6  2730  fun11iun  5147  poxp  5853  smoel  5915  iinerm  6178  prarloclemlo  6592  peano5uzti  8346  lbzbi  8551  ssfzo12bi  9081  cau3lem  9710  nn0seqcvgd  9880
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