Theorem anabsi8 685

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 682	. 2 ⊢ ((𝜓 ∧ 𝜑) → 𝜒)
3	2	ancoms 464	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)

This proof depends on syntax axioms:   → wi 4   ∧ wa 401

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402

This theorem is used by:  subuhgr  29867  subupgr  29868  subumgr  29869  subusgr  29870