Theorem 3impd 1165

Description: Importation deduction for triple conjunction. (Contributed by NM, 26-Oct-2006.)

Hypothesis

Ref	Expression
3imp1.1	⊢ (φ → (ψ → (χ → (θ → τ))))

Assertion

Ref	Expression
3impd	⊢ (φ → ((ψ ∧ χ ∧ θ) → τ))

Proof of Theorem 3impd

Step	Hyp	Ref	Expression
1		3imp1.1	. . . 4 ⊢ (φ → (ψ → (χ → (θ → τ))))
2	1	com4l 78	. . 3 ⊢ (ψ → (χ → (θ → (φ → τ))))
3	2	3imp 1145	. 2 ⊢ ((ψ ∧ χ ∧ θ) → (φ → τ))
4	3	com12 27	1 ⊢ (φ → ((ψ ∧ χ ∧ θ) → τ))

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  5518  funsi  5521  oprabid  5551  fntxp  5805  fnpprod  5844