Theorem expimpd 586

Description: Exportation followed by a deduction version of importation. (Contributed by NM, 6-Sep-2008.)

Hypothesis

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

Assertion

Ref	Expression
expimpd	⊢ (φ → ((ψ ∧ χ) → θ))

Proof of Theorem expimpd

Step	Hyp	Ref	Expression
1		expimpd.1	. . 3 ⊢ ((φ ∧ ψ) → (χ → θ))
2	1	ex 423	. 2 ⊢ (φ → (ψ → (χ → θ)))
3	2	imp3a 420	1 ⊢ (φ → ((ψ ∧ χ) → θ))

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:  tfindi  4496  elpreima  5407  enmap2lem3  6065  enmap1lem3  6071  ncdisjun  6136  ncssfin  6151  leltctr  6212  letc  6231  nchoicelem8  6296  nchoicelem12  6300