Theorem 3expib 1154

Description: Exportation from triple conjunction. (Contributed by NM, 19-May-2007.)

Hypothesis

Ref	Expression
3exp.1	⊢ ((φ ∧ ψ ∧ χ) → θ)

Assertion

Ref	Expression
3expib	⊢ (φ → ((ψ ∧ χ) → θ))

Proof of Theorem 3expib

Step	Hyp	Ref	Expression
1		3exp.1	. . 3 ⊢ ((φ ∧ ψ ∧ χ) → θ)
2	1	3exp 1150	. 2 ⊢ (φ → (ψ → (χ → θ)))
3	2	imp3a 420	1 ⊢ (φ → ((ψ ∧ χ) → θ))

Syntax hints:   → wi 4   ∧ wa 358   ∧ w3a 934

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  df-3an 936

This theorem is referenced by:  3anidm12  1239  mob  3019  fco  5232  f1oiso2  5501  fntxp  5805  fnpprod  5844  clos1is  5882  connexrd  5931  3ecoptocl  5999  enpw1  6063  enprmaplem3  6079  nchoicelem6  6295