Theorem 3impdi 1369

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 691	. 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃)
3	2	3impb 1132	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)

This proof depends on syntax axioms:   → wi 4   ∧ wa 401   ∧ w3a 1103

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105

This theorem is used by:  oacan  8560  omcan  8581  ecovdi  8850  distrpi  10987  axltadd  11387  ccatlcan  14872  absmulgcd  16728  axlowdimlem14  29539  fh1  32226  fh2  32227  cm2j  32228  hoadddi  32411  hosubdi  32416  leopmul2i  32743  dvconstbi  45412  eel2131  45790  uun2131  45867  uun2131p1  45868  io1ii  50129  reccot  51020  rectan  51021