Theorem anass1rs 652

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 649	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 206  df-an 396

This theorem is referenced by:  sossfld  6185  1stconst  8089  infunsdom  10212  creui  12212  qreccl  12958  fsumrlim  15762  fsumo1  15763  climfsum  15771  imasvscaf  17490  grppropd  18874  grpinvpropd  18935  cycsubgcl  19122  frgpup1  19685  ringrghm  20202  phlpropd  21428  mamuass  22123  iccpnfcnv  24690  mbfeqalem1  25391  mbfinf  25415  mbflimsup  25416  mbflimlem  25417  itgfsum  25577  plypf1  25962  mtest  26153  rpvmasum2  27252  ifeqeqx  32042  ordtconnlem1  33203  xrge0iifcnv  33212  fsum2dsub  33918  fvineqsneu  36596  pibt2  36602  incsequz  36920  equivtotbnd  36950  intidl  37201  keridl  37204  prnc  37239  cdleme50trn123  39729  dva1dim  40160  dia1dim2  40237  3factsumint1  41193