Theorem anabsi7 670

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 669	. 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  840  nelrdva  3727  elunii  4936  ordelord  6417  fvelrn  7110  onsucuni2  7870  fnfi  9244  prnmax  11064  relexpindlem  15112  opreu2reuALT  32505  ralssiun  37373  monotoddzz  42900  oddcomabszz  42901  flcidc  43131  fmul01  45501  fprodcnlem  45520  stoweidlem4  45925  stoweidlem20  45941  stoweidlem22  45943  stoweidlem27  45948  stoweidlem30  45951  stoweidlem51  45972  stoweidlem59  45980  fourierdlem21  46049  fourierdlem89  46116  fourierdlem90  46117  fourierdlem91  46118  fourierdlem104  46131