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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))

Colors of variables: wff setvar class

Syntax hints: → wi 4 ∧ wa 358

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 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