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  6183  1stconst  8083  infunsdom  10206  creui  12204  qreccl  12950  fsumrlim  15754  fsumo1  15755  climfsum  15763  imasvscaf  17482  grppropd  18834  grpinvpropd  18895  cycsubgcl  19078  frgpup1  19638  ringrghm  20119  phlpropd  21200  mamuass  21894  iccpnfcnv  24452  mbfeqalem1  25150  mbfinf  25174  mbflimsup  25175  mbflimlem  25176  itgfsum  25336  plypf1  25718  mtest  25908  rpvmasum2  27005  ifeqeqx  31762  ordtconnlem1  32893  xrge0iifcnv  32902  fsum2dsub  33608  fvineqsneu  36281  pibt2  36287  incsequz  36605  equivtotbnd  36635  intidl  36886  keridl  36889  prnc  36924  cdleme50trn123  39414  dva1dim  39845  dia1dim2  39922  3factsumint1  40875