Theorem 3impdi 630

Description: Importation inference (undistribute conjunction).

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 394	. 2 ⊢ ((φ ∧ (ψ ∧ χ)) → θ)
3	2	3impb 610	1 ⊢ ((φ ∧ ψ ∧ χ) → θ)

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

This theorem is referenced by:  oacan 3150  nnmcan 3190  ecoprdi 3257  distrpi 3820  distrpqlem 3860

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

metamath.org