Theorem rp-simp2 42220

Description: Simplification of triple conjunction. Identical to simp2 1137. (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 42219	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜓)))
2	1	3imp 1111	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜓)

Syntax hints:   → wi 4   ∧ w3a 1087

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege1 42217

This theorem depends on definitions:  df-bi 206  df-an 397  df-3an 1089

This theorem is referenced by:  ntrclsk3  42497