Theorem simp-8r 803

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

Assertion

Ref	Expression
simp-8r	⊢ (((((((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) → 𝜓)

Proof of Theorem simp-8r

Step	Hyp	Ref	Expression
1		id 23	. 2 ⊢ (𝜓 → 𝜓)
2	1	ad8antlr 753	1 ⊢ (((((((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 400

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 210  df-an 401

This theorem is referenced by:  chnso  18670  ssdifidlprm  21446  2sqmo  27559  legso  28826  opphl  28985  f1otrg  29129  2ndresdju  32906  cyc3conja  33390  rloccring  33504  mxidlprm  33670  mxidlirred  33672  constrconj  34052  constrfin  34053  constrelextdg2  34054  cos9thpiminplylem2  34090  qtophaus  34143  esumcst  34370  dffltz  43228  smfmullem3  47365