Theorem simp-9r 806

Description: Simplification of a conjunction. (Contributed by Mario Carneiro, 4-Jan-2017.) (Proof shortened by Wolf Lammen, 24-May-2022.)

Assertion

Ref	Expression
simp-9r	⊢ ((((((((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) → 𝜓)

Proof of Theorem simp-9r

Step	Hyp	Ref	Expression
1		id 23	. 2 ⊢ (𝜓 → 𝜓)
2	1	ad9antlr 756	1 ⊢ ((((((((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) → 𝜓)

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:  legso  28905  miriso  28984  footexALT  29035  footex  29038  prlngmolem2  29240  f1otrg  29257  2ndresdju  33031  rloccring  33622  qsdrngi  33808  1arithidom  33858  constrfin  34167