Theorem anabsi8 669

Description: Absorption of antecedent into conjunction. (Contributed by NM, 26-Sep-1999.)

Hypothesis

Ref	Expression
anabsi8.1	⊢ (𝜓 → ((𝜓 ∧ 𝜑) → 𝜒))

Assertion

Ref	Expression
anabsi8	⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Proof of Theorem anabsi8

Step	Hyp	Ref	Expression
1		anabsi8.1	. . 3 ⊢ (𝜓 → ((𝜓 ∧ 𝜑) → 𝜒))
2	1	anabsi5 666	. 2 ⊢ ((𝜓 ∧ 𝜑) → 𝜒)
3	2	ancoms 459	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 396

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 397

This theorem is referenced by:  subuhgr  27653  subupgr  27654  subumgr  27655  subusgr  27656