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  6162  1stconst  8082  infunsdom  10173  creui  12188  qreccl  12935  fsumrlim  15784  fsumo1  15785  climfsum  15793  imasvscaf  17509  grppropd  18890  grpinvpropd  18954  cycsubgcl  19145  frgpup1  19712  ringrghm  20229  phlpropd  21571  mamuass  22296  iccpnfcnv  24849  mbfeqalem1  25549  mbfinf  25573  mbflimsup  25574  mbflimlem  25575  itgfsum  25735  plypf1  26124  mtest  26320  rpvmasum2  27430  ifeqeqx  32478  ordtconnlem1  33921  xrge0iifcnv  33930  fsum2dsub  34605  fvineqsneu  37406  pibt2  37412  incsequz  37749  equivtotbnd  37779  intidl  38030  keridl  38033  prnc  38068  cdleme50trn123  40555  dva1dim  40986  dia1dim2  41063  3factsumint1  42016  modelac8prim  44989