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 → (θ → τ))))

Proof of Theorem 3expd

Step	Hyp	Ref	Expression
1		3expd.1	. . . 4 ⊢ (φ → ((ψ ∧ χ ∧ θ) → τ))
2	1	com12 27	. . 3 ⊢ ((ψ ∧ χ ∧ θ) → (φ → τ))
3	2	3exp 1150	. 2 ⊢ (ψ → (χ → (θ → (φ → τ))))
4	3	com4r 80	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:  3exp2  1169  exp516  1171  3impexp  1366  3impexpbicom  1367