Theorem simp-8r 791

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 741	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  18547  2sqmo  27404  legso  28671  opphl  28826  f1otrg  28943  2ndresdju  32727  cyc3conja  33239  rloccring  33352  ssdifidlprm  33539  mxidlprm  33551  mxidlirred  33553  constrconj  33902  constrfin  33903  constrelextdg2  33904  cos9thpiminplylem2  33940  qtophaus  33993  esumcst  34220  dffltz  42873  smfmullem3  47033