Theorem anass1rs 655

Description: Commutative-associative law for conjunction in an antecedent. (Contributed by Jeff Madsen, 19-Jun-2011.)

Hypothesis

Ref	Expression
anass1rs.1	⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃)

Assertion

Ref	Expression
anass1rs	⊢ (((𝜑 ∧ 𝜒) ∧ 𝜓) → 𝜃)

Proof of Theorem anass1rs

Step	Hyp	Ref	Expression
1		anass1rs.1	. . 3 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃)
2	1	anassrs 467	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃)
3	2	an32s 652	1 ⊢ (((𝜑 ∧ 𝜒) ∧ 𝜓) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 395

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

This theorem is referenced by:  sossfld  6205  1stconst  8126  infunsdom  10254  creui  12262  qreccl  13012  fsumrlim  15848  fsumo1  15849  climfsum  15857  imasvscaf  17585  grppropd  18970  grpinvpropd  19034  cycsubgcl  19225  frgpup1  19794  ringrghm  20311  phlpropd  21674  mamuass  22407  iccpnfcnv  24976  mbfeqalem1  25677  mbfinf  25701  mbflimsup  25702  mbflimlem  25703  itgfsum  25863  plypf1  26252  mtest  26448  rpvmasum2  27557  ifeqeqx  32556  ordtconnlem1  33924  xrge0iifcnv  33933  fsum2dsub  34623  fvineqsneu  37413  pibt2  37419  incsequz  37756  equivtotbnd  37786  intidl  38037  keridl  38040  prnc  38075  cdleme50trn123  40557  dva1dim  40988  dia1dim2  41065  3factsumint1  42023  modelac8prim  45014