Theorem imp5g 583

Description: An importation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)

Hypothesis

Ref	Expression
imp5.1	⊢ (φ → (ψ → (χ → (θ → (τ → η)))))

Assertion

Ref	Expression
imp5g	⊢ ((φ ∧ ψ) → (((χ ∧ θ) ∧ τ) → η))

Proof of Theorem imp5g

Step	Hyp	Ref	Expression
1		imp5.1	. . 3 ⊢ (φ → (ψ → (χ → (θ → (τ → η)))))
2	1	imp 418	. 2 ⊢ ((φ ∧ ψ) → (χ → (θ → (τ → η))))
3	2	imp4c 574	1 ⊢ ((φ ∧ ψ) → (((χ ∧ θ) ∧ τ) → η))

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)