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Theorem expdimp 426

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

**Hypothesis**
Ref	Expression
exp3a.1	⊢ (φ → ((ψ ∧ χ) → θ))

**Assertion**
Ref	Expression
expdimp	⊢ ((φ ∧ ψ) → (χ → θ))

**Proof of Theorem expdimp**
Step	Hyp	Ref	Expression
1		exp3a.1	. . 3 ⊢ (φ → ((ψ ∧ χ) → θ))
2	1	exp3a 425	. 2 ⊢ (φ → (ψ → (χ → θ)))
3	2	imp 418	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: rexlimdvv 2744 ralcom2 2775 reu6 3025 preaddccan2 4455 ltfinasym 4460 lenltfin 4469 vfinspsslem1 4550 phi11lem1 4595 fun11iun 5305 erth 5968 ltlenlec 6207 leltctr 6212 tlecg 6230