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:  2sqmo  27364  legso  28562  opphl  28717  f1otrg  28834  2ndresdju  32606  chnso  32969  cyc3conja  33112  rloccring  33220  ssdifidlprm  33405  mxidlprm  33417  mxidlirred  33419  constrconj  33711  constrfin  33712  constrelextdg2  33713  cos9thpiminplylem2  33749  qtophaus  33802  esumcst  34029  dffltz  42607  smfmullem3  46775