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Theorem 3impd 1165
Description: Importation deduction for triple conjunction. (Contributed by NM, 26-Oct-2006.)
Hypothesis
Ref Expression
3imp1.1 (φ → (ψ → (χ → (θτ))))
Assertion
Ref Expression
3impd (φ → ((ψ χ θ) → τ))

Proof of Theorem 3impd
StepHypRef Expression
1 3imp1.1 . . . 4 (φ → (ψ → (χ → (θτ))))
21com4l 78 . . 3 (ψ → (χ → (θ → (φτ))))
323imp 1145 . 2 ((ψ χ θ) → (φτ))
43com12 27 1 (φ → ((ψ χ θ) → τ))
Colors of variables: wff setvar class
Syntax hints:  wi 4   w3a 934
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
This theorem is referenced by:  3imp2  1166  3impexp  1366  fununiq  5517  funsi  5520  oprabid  5550  fntxp  5804  fnpprod  5843
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