Theorem 3impdir 1351

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 678	. 2 ⊢ (((𝜑 ∧ 𝜒) ∧ 𝜓) → 𝜃)
3	2	3impa 1110	1 ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜓) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1087

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1089

This theorem is referenced by:  divcan7  12003  ccatrcan  14767  his7  31122  his2sub2  31125  hoadddir  31836  nndivsub  36423  rdgeqoa  37336  eel3132  44686  3impdirp1  44787