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Theorem 3expd 1168
Description: Exportation deduction for triple conjunction. (Contributed by NM, 26-Oct-2006.)
Hypothesis
Ref Expression
3expd.1 (φ → ((ψ χ θ) → τ))
Assertion
Ref Expression
3expd (φ → (ψ → (χ → (θτ))))

Proof of Theorem 3expd
StepHypRef Expression
1 3expd.1 . . . 4 (φ → ((ψ χ θ) → τ))
21com12 27 . . 3 ((ψ χ θ) → (φτ))
323exp 1150 . 2 (ψ → (χ → (θ → (φτ))))
43com4r 80 1 (φ → (ψ → (χ → (θτ))))
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:  3exp2  1169  exp516  1171  3impexp  1366  3impexpbicom  1367
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