Theorem imp31 421

Description: An importation inference. (Contributed by NM, 26-Apr-1994.)

Hypothesis

Ref	Expression
imp3.1	⊢ (φ → (ψ → (χ → θ)))

Assertion

Ref	Expression
imp31	⊢ (((φ ∧ ψ) ∧ χ) → θ)

Proof of Theorem imp31

Step	Hyp	Ref	Expression
1		imp3.1	. . 3 ⊢ (φ → (ψ → (χ → θ)))
2	1	imp 418	. 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:  imp41  576  imp5d  582  impl  603  anassrs  629  an31s  781  3imp  1145  3expa  1151  ncfinraise  4482  evenodddisj  4517  funimass3  5405