Theorem 3exp1 1167

Description: Exportation from left triple conjunction. (Contributed by NM, 24-Feb-2005.)

Hypothesis

Ref	Expression
3exp1.1	⊢ (((φ ∧ ψ ∧ χ) ∧ θ) → τ)

Assertion

Ref	Expression
3exp1	⊢ (φ → (ψ → (χ → (θ → τ))))

Proof of Theorem 3exp1

Step	Hyp	Ref	Expression
1		3exp1.1	. . 3 ⊢ (((φ ∧ ψ ∧ χ) ∧ θ) → τ)
2	1	ex 423	. 2 ⊢ ((φ ∧ ψ ∧ χ) → (θ → τ))
3	2	3exp 1150	1 ⊢ (φ → (ψ → (χ → (θ → τ))))

Syntax hints:   → wi 4   ∧ wa 358   ∧ 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: (None)