Theorem 3impdi 1237

Description: Importation inference (undistribute conjunction). (Contributed by NM, 14-Aug-1995.)

Hypothesis

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

Assertion

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

Proof of Theorem 3impdi

Step	Hyp	Ref	Expression
1		3impdi.1	. . 3 ⊢ (((φ ∧ ψ) ∧ (φ ∧ χ)) → θ)
2	1	anandis 803	. 2 ⊢ ((φ ∧ (ψ ∧ χ)) → θ)
3	2	3impb 1147	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: (None)