Theorem 3impdir 1191

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 527	. 2 ⊢ (((𝜑 ∧ 𝜒) ∧ 𝜓) → 𝜃)
3	2	3impa 1099	1 ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜓) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 97   ∧ w3a 885

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-3an 887

This theorem is referenced by:  nnanq0  6556  divcanap7  7697