Theorem simp-7r 789

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

Assertion

Ref	Expression
simp-7r	⊢ ((((((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) → 𝜓)

Proof of Theorem simp-7r

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ (𝜓 → 𝜓)
2	1	ad7antlr 739	1 ⊢ ((((((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) → 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:  catass  17698  2sqmo  27400  tgbtwnconn1  28554  legso  28578  miriso  28649  footexALT  28697  footex  28700  opphl  28733  lnopp2hpgb  28742  f1otrg  28850  2ndresdju  32627  cyc3genpm  33163  cyc3conja  33168  rloccring  33265  isprmidlc  33462  ssdifidlprm  33473  mxidlprm  33485  qsdrngi  33510  1arithidom  33552  fldext2chn  33762  constrconj  33779  constrfin  33780  constrelextdg2  33781  zarcmplem  33912  afsval  34703  dffltz  42657  smfmullem3  46822