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Theorem exp43 364
Description: An exportation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
exp43.1 (((𝜑𝜓) ∧ (𝜒𝜃)) → 𝜏)
Assertion
Ref Expression
exp43 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))

Proof of Theorem exp43
StepHypRef Expression
1 exp43.1 . . 3 (((𝜑𝜓) ∧ (𝜒𝜃)) → 𝜏)
21ex 113 . 2 ((𝜑𝜓) → ((𝜒𝜃) → 𝜏))
32exp4b 359 1 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  exp53  369  funssres  5056  fvopab3ig  5378  fvmptt  5394  tfri3  6132  nnmordi  6273  fiintim  6637  ordiso2  6726  qaddcl  9118  qmulcl  9120  bernneq  10070
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