Theorem 3impdir 883

Description: Importation inference (undistribute conjunction).

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 515	. 2 ⊢ (((φ ⋀ χ) ⋀ ψ) → θ)
3	2	3impa 830	1 ⊢ ((φ ⋀ χ ⋀ ψ) → θ)

Syntax hints:   → wi 3   ⋀ wa 223   ⋀ w3a 777

This theorem is referenced by:  his7t 8951  his2sub2t 8954  hoadddirt 9725  nndivsub 10416

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225  df-3an 779

Copyright terms: Public domain