Theorem 3impib 1204

Description: Importation to triple conjunction. (Contributed by NM, 13-Jun-2006.)

Hypothesis

Ref	Expression
3impib.1	⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃))

Assertion

Ref	Expression
3impib	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)

Proof of Theorem 3impib

Step	Hyp	Ref	Expression
1		3impib.1	. . 3 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃))
2	1	expd 258	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
3	2	3imp 1196	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 981

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 983

This theorem is referenced by:  mob  2956  eqreu  2966  iotam  5268  funimaexglem  5362  ssimaexg  5648  funopdmsn  5771  rbropap  6336  dfsmo2  6380  3ecoptocl  6718  distrnq0  7579  addassnq0  7582  uzind  9491  fzind  9495  fnn0ind  9496  xltnegi  9964  facwordi  10892  shftvalg  11191  shftval4g  11192  mulgcd  12381  coprmdvds1  12457  pcfac  12717  mgmcl  13235  mhmlin  13343  mhmmulg  13543  issubg2m  13569  nsgbi  13584  srgmulgass  13795  dvdsrtr  13907  issubrng2  14016  issubrg2  14047  domnmuln0  14079  inopn  14519  basis1  14563  cnmpt2t  14809  cnmpt22  14810  cnmptcom  14814  xmeteq0  14875  sincosq1sgn  15342  sincosq2sgn  15343  sincosq3sgn  15344  sincosq4sgn  15345  speano5  15954