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  6208  1stconst  8124  infunsdom  10251  creui  12259  qreccl  13009  fsumrlim  15844  fsumo1  15845  climfsum  15853  imasvscaf  17586  grppropd  18982  grpinvpropd  19046  cycsubgcl  19237  frgpup1  19808  ringrghm  20327  phlpropd  21691  mamuass  22422  iccpnfcnv  24989  mbfeqalem1  25690  mbfinf  25714  mbflimsup  25715  mbflimlem  25716  itgfsum  25877  plypf1  26266  mtest  26462  rpvmasum2  27571  ifeqeqx  32563  ordtconnlem1  33885  xrge0iifcnv  33894  fsum2dsub  34601  fvineqsneu  37394  pibt2  37400  incsequz  37735  equivtotbnd  37765  intidl  38016  keridl  38019  prnc  38054  cdleme50trn123  40537  dva1dim  40968  dia1dim2  41045  3factsumint1  42003