Theorem exp4b 590

Description: An exportation inference. (Contributed by NM, 26-Apr-1994.) (Proof shortened by Wolf Lammen, 23-Nov-2012.)

Hypothesis

Ref	Expression
exp4b.1	⊢ ((φ ∧ ψ) → ((χ ∧ θ) → τ))

Assertion

Ref	Expression
exp4b	⊢ (φ → (ψ → (χ → (θ → τ))))

Proof of Theorem exp4b

Step	Hyp	Ref	Expression
1		exp4b.1	. . 3 ⊢ ((φ ∧ ψ) → ((χ ∧ θ) → τ))
2	1	ex 423	. 2 ⊢ (φ → (ψ → ((χ ∧ θ) → τ)))
3	2	exp4a 589	1 ⊢ (φ → (ψ → (χ → (θ → τ))))

Syntax hints:   → wi 4   ∧ wa 358

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

This theorem is referenced by:  exp43  595  reuss2  3536  nchoicelem17  6306