Theorem 3impdi 1352

Description: Importation inference (undistribute conjunction). (Contributed by NM, 14-Aug-1995.)

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 679	. 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃)
3	2	3impb 1115	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 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:  oacan  8485  omcan  8506  ecovdi  8774  distrpi  10821  axltadd  11218  ccatlcan  14653  absmulgcd  16488  axlowdimlem14  29040  fh1  31705  fh2  31706  cm2j  31707  hoadddi  31890  hosubdi  31895  leopmul2i  32222  dvconstbi  44687  eel2131  45066  uun2131  45143  uun2131p1  45144  io1ii  49277  reccot  50114  rectan  50115