Theorem anabsi7 672

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 671	. 2 ⊢ ((𝜓 ∧ 𝜑) → 𝜒)
3	2	ancoms 458	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)

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:  syldbl2  842  nelrdva  3664  elunii  4869  ordelord  6340  fvelrn  7023  onsucuni2  7778  fnfi  9106  prnmax  10910  relexpindlem  14990  opreu2reuALT  32554  ralssiun  37614  monotoddzz  43252  oddcomabszz  43253  flcidc  43479  fmul01  45893  fprodcnlem  45912  stoweidlem4  46315  stoweidlem20  46331  stoweidlem22  46333  stoweidlem27  46338  stoweidlem30  46341  stoweidlem51  46362  stoweidlem59  46370  fourierdlem21  46439  fourierdlem89  46506  fourierdlem90  46507  fourierdlem91  46508  fourierdlem104  46521