Theorem imp43 578

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

Hypothesis

Ref	Expression
imp4.1	⊢ (φ → (ψ → (χ → (θ → τ))))

Assertion

Ref	Expression
imp43	⊢ (((φ ∧ ψ) ∧ (χ ∧ θ)) → τ)

Proof of Theorem imp43

Step	Hyp	Ref	Expression
1		imp4.1	. . 3 ⊢ (φ → (ψ → (χ → (θ → τ))))
2	1	imp4b 573	. 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

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)