Theorem 3imp2 1166

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

Hypothesis

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

Assertion

Ref	Expression
3imp2	⊢ ((φ ∧ (ψ ∧ χ ∧ θ)) → τ)

Proof of Theorem 3imp2

Step	Hyp	Ref	Expression
1		3imp1.1	. . 3 ⊢ (φ → (ψ → (χ → (θ → τ))))
2	1	3impd 1165	. 2 ⊢ (φ → ((ψ ∧ χ ∧ θ) → τ))
3	2	imp 418	1 ⊢ ((φ ∧ (ψ ∧ χ ∧ θ)) → τ)

This proof depends on syntax axioms:   → wi 4   ∧ wa 358   ∧ w3a 934

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360  df-3an 936

This theorem is used by: (None)