Theorem exp41 593

Description: An exportation inference. (Contributed by NM, 26-Apr-1994.)

Hypothesis

Ref	Expression
exp41.1	⊢ ((((φ ∧ ψ) ∧ χ) ∧ θ) → τ)

Assertion

Ref	Expression
exp41	⊢ (φ → (ψ → (χ → (θ → τ))))

Proof of Theorem exp41

Step	Hyp	Ref	Expression
1		exp41.1	. . 3 ⊢ ((((φ ∧ ψ) ∧ χ) ∧ θ) → τ)
2	1	ex 423	. 2 ⊢ (((φ ∧ ψ) ∧ χ) → (θ → τ))
3	2	exp31 587	1 ⊢ (φ → (ψ → (χ → (θ → τ))))

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

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

This theorem is used by: (None)