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  8515  omcan  8536  ecovdi  8801  distrpi  10858  axltadd  11254  ccatlcan  14690  absmulgcd  16526  axlowdimlem14  28889  fh1  31554  fh2  31555  cm2j  31556  hoadddi  31739  hosubdi  31744  leopmul2i  32071  dvconstbi  44330  eel2131  44710  uun2131  44787  uun2131p1  44788  io1ii  48913  reccot  49751  rectan  49752