Theorem 3impib 1149

Description: Importation to triple conjunction. (Contributed by NM, 13-Jun-2006.)

Hypothesis

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

Assertion

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

Proof of Theorem 3impib

Step	Hyp	Ref	Expression
1		3impib.1	. . 3 ⊢ (φ → ((ψ ∧ χ) → θ))
2	1	exp3a 425	. 2 ⊢ (φ → (ψ → (χ → θ)))
3	2	3imp 1145	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:  mob  3018  eqreu  3028  dedth3h  3705  peano5  4409  ncfinraise  4481  ncfinlower  4483  nnpweq  4523  spfininduct  4540  clos1induct  5880  3ecoptocl  5998  sbthlem2  6204