Theorem simp-8r 792

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 22	. 2 ⊢ (𝜓 → 𝜓)
2	1	ad8antlr 742	1 ⊢ (((((((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 395

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 207  df-an 396

This theorem is referenced by:  chnso  18559  2sqmo  27416  legso  28683  opphl  28838  f1otrg  28955  2ndresdju  32738  cyc3conja  33250  rloccring  33363  ssdifidlprm  33550  mxidlprm  33562  mxidlirred  33564  constrconj  33922  constrfin  33923  constrelextdg2  33924  cos9thpiminplylem2  33960  qtophaus  34013  esumcst  34240  dffltz  42986  smfmullem3  47145