Theorem 3impdir 1238

Description: Importation inference (undistribute conjunction). (Contributed by NM, 20-Aug-1995.)

Hypothesis

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

Assertion

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

Proof of Theorem 3impdir

Step	Hyp	Ref	Expression
1		3impdir.1	. . 3 ⊢ (((φ ∧ ψ) ∧ (χ ∧ ψ)) → θ)
2	1	anandirs 804	. 2 ⊢ (((φ ∧ χ) ∧ ψ) → θ)
3	2	3impa 1146	1 ⊢ ((φ ∧ χ ∧ ψ) → 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: (None)