Theorem anabsi7 669

Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 18-Nov-2013.)

Hypothesis

Ref	Expression
anabsi7.1	⊢ (𝜓 → ((𝜑 ∧ 𝜓) → 𝜒))

Assertion

Ref	Expression
anabsi7	⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Proof of Theorem anabsi7

Step	Hyp	Ref	Expression
1		anabsi7.1	. . 3 ⊢ (𝜓 → ((𝜑 ∧ 𝜓) → 𝜒))
2	1	anabsi6 668	. 2 ⊢ ((𝜓 ∧ 𝜑) → 𝜒)
3	2	ancoms 459	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 396

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 397

This theorem is referenced by:  syldbl2  839  nelrdva  3697  elunii  4906  ordelord  6375  fvelrn  7063  onsucuni2  7805  fnfi  9164  prnmax  10972  relexpindlem  14992  opreu2reuALT  31580  ralssiun  36092  monotoddzz  41453  oddcomabszz  41454  flcidc  41687  fmul01  44069  fprodcnlem  44088  stoweidlem4  44493  stoweidlem20  44509  stoweidlem22  44511  stoweidlem27  44516  stoweidlem30  44519  stoweidlem51  44540  stoweidlem59  44548  fourierdlem21  44617  fourierdlem89  44684  fourierdlem90  44685  fourierdlem91  44686  fourierdlem104  44699