Theorem 3impdi 1351

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 678	. 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃)
3	2	3impb 1114	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1086

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 1088

This theorem is referenced by:  oacan  8473  omcan  8494  ecovdi  8759  distrpi  10811  axltadd  11208  ccatlcan  14643  absmulgcd  16479  axlowdimlem14  28919  fh1  31581  fh2  31582  cm2j  31583  hoadddi  31766  hosubdi  31771  leopmul2i  32098  dvconstbi  44327  eel2131  44707  uun2131  44784  uun2131p1  44785  io1ii  48925  reccot  49763  rectan  49764