Theorem rp-simp2 44547

Description: Simplification of triple conjunction. Identical to simp2 1154. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
rp-simp2	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜓)

Proof of Theorem rp-simp2

Step	Hyp	Ref	Expression
1		rp-simp2-frege 44546	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜓)))
2	1	3imp 1127	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜓)

This proof depends on syntax axioms:   → wi 4   ∧ w3a 1102

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege1 44544

This proof depends on definitions:  df-bi 210  df-an 401  df-3an 1104

This theorem is used by:  ntrclsk3  44824