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Theorem exp4b 349
 Description: An exportation inference. (Contributed by NM, 26-Apr-1994.) (Proof shortened by Wolf Lammen, 23-Nov-2012.)
Hypothesis
Ref Expression
exp4b.1 ((φ ψ) → ((χ θ) → τ))
Assertion
Ref Expression
exp4b (φ → (ψ → (χ → (θτ))))

Proof of Theorem exp4b
StepHypRef Expression
1 exp4b.1 . . 3 ((φ ψ) → ((χ θ) → τ))
21ex 108 . 2 (φ → (ψ → ((χ θ) → τ)))
32exp4a 348 1 (φ → (ψ → (χ → (θτ))))
 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 depends on definitions:  df-bi 110 This theorem is referenced by:  exp43  354  reuss2  3211  nndi  6004  mulnqprl  6549  mulnqpru  6550  distrlem5prl  6562  distrlem5pru  6563  recexprlemss1l  6607  recexprlemss1u  6608  lemul12a  7609  nnmulcl  7716  elfz0fzfz0  8753  fzo1fzo0n0  8809  fzofzim  8814  elfzodifsumelfzo  8827  le2sq2  8982
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