Theorem anabsi7 545

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 544	. 2 ⊢ ((𝜓 ∧ 𝜑) → 𝜒)
3	2	ancoms 264	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  syl2an23an  1230  nelrdva  2797  elunii  3606  ordelord  4136  onsucuni2  4307  funfveu  5208  fvelrn  5319  phplem3g  6342  prdisj  6682  gcdmultiplez  10410  dvdssq  10420