Theorem anass1rs 654

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 469	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃)
3	2	an32s 651	1 ⊢ (((𝜑 ∧ 𝜒) ∧ 𝜓) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 397

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 398

This theorem is referenced by:  sossfld  6186  1stconst  8086  infunsdom  10209  creui  12207  qreccl  12953  fsumrlim  15757  fsumo1  15758  climfsum  15766  imasvscaf  17485  grppropd  18837  grpinvpropd  18898  cycsubgcl  19083  frgpup1  19643  ringrghm  20125  phlpropd  21208  mamuass  21902  iccpnfcnv  24460  mbfeqalem1  25158  mbfinf  25182  mbflimsup  25183  mbflimlem  25184  itgfsum  25344  plypf1  25726  mtest  25916  rpvmasum2  27015  ifeqeqx  31774  ordtconnlem1  32904  xrge0iifcnv  32913  fsum2dsub  33619  fvineqsneu  36292  pibt2  36298  incsequz  36616  equivtotbnd  36646  intidl  36897  keridl  36900  prnc  36935  cdleme50trn123  39425  dva1dim  39856  dia1dim2  39933  3factsumint1  40886