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 460	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)

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:  syldbl2  840  nelrdva  3702  elunii  4914  ordelord  6387  fvelrn  7079  onsucuni2  7822  fnfi  9181  prnmax  10990  relexpindlem  15010  opreu2reuALT  31748  ralssiun  36336  monotoddzz  41730  oddcomabszz  41731  flcidc  41964  fmul01  44344  fprodcnlem  44363  stoweidlem4  44768  stoweidlem20  44784  stoweidlem22  44786  stoweidlem27  44791  stoweidlem30  44794  stoweidlem51  44815  stoweidlem59  44823  fourierdlem21  44892  fourierdlem89  44959  fourierdlem90  44960  fourierdlem91  44961  fourierdlem104  44974