Theorem 3expb 1152

Description: Exportation from triple to double conjunction. (Contributed by NM, 20-Aug-1995.)

Hypothesis

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

Assertion

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

Proof of Theorem 3expb

Step	Hyp	Ref	Expression
1		3exp.1	. . 3 ⊢ ((φ ∧ ψ ∧ χ) → θ)
2	1	3exp 1150	. 2 ⊢ (φ → (ψ → (χ → θ)))
3	2	imp32 422	1 ⊢ ((φ ∧ (ψ ∧ χ)) → θ)

This proof depends on syntax axioms:   → wi 4   ∧ wa 358   ∧ w3a 934

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  df-3an 936

This theorem is used by:  3adant3r1  1160  3adant3r2  1161  3adant3r3  1162  3adant1l  1174  3adant1r  1175  mp3an1  1264  sfin112  4530  fnfco  5238  fununiq  5518  mpt2eq3dva  5670  peano4nc  6151