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  8535  omcan  8556  ecovdi  8825  distrpi  10907  axltadd  11307  ccatlcan  14787  absmulgcd  16639  axlowdimlem14  29412  fh1  32099  fh2  32100  cm2j  32101  hoadddi  32284  hosubdi  32289  leopmul2i  32616  dvconstbi  45158  eel2131  45536  uun2131  45613  uun2131p1  45614  io1ii  49847  reccot  50684  rectan  50685