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))

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:  rexlimdvv  2745  ralcom2  2776  reu6  3026  preaddccan2  4456  ltfinasym  4461  lenltfin  4470  vfinspsslem1  4551  phi11lem1  4596  fun11iun  5306  erth  5969  ltlenlec  6208  leltctr  6213  tlecg  6231