Theorem 3impdir 631

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 395	. 2 ⊢ (((φ ∧ χ) ∧ ψ) → θ)
3	2	3impa 609	1 ⊢ ((φ ∧ χ ∧ ψ) → θ)

Syntax hints:   → wi 2   ∧ wa 196   ∧ w3a 581

This theorem is referenced by:  his7 5051

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

This theorem depends on definitions:  df-bi 128  df-an 198  df-3an 583

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