Theorem anabss1 662

Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 31-Dec-2012.)

Hypothesis

Ref	Expression
anabss1.1	⊢ (((𝜑 ∧ 𝜓) ∧ 𝜑) → 𝜒)

Assertion

Ref	Expression
anabss1	⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Proof of Theorem anabss1

Step	Hyp	Ref	Expression
1		anabss1.1	. . 3 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜑) → 𝜒)
2	1	an32s 648	. 2 ⊢ (((𝜑 ∧ 𝜑) ∧ 𝜓) → 𝜒)
3	2	anabsan 661	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 206  df-an 396

This theorem is referenced by:  anabss4  663  ordtri3or  6283  onfununi  8143  omordi  8359  oeoelem  8391  hashssdif  14055  fzindd  39912  nzss  41824  stirlinglem5  43509