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  17579  2sqmo  27329  tgbtwnconn1  28507  legso  28531  miriso  28602  footexALT  28650  footex  28653  opphl  28686  lnopp2hpgb  28695  f1otrg  28803  2ndresdju  32583  cyc3genpm  33089  cyc3conja  33094  rloccring  33205  isprmidlc  33380  ssdifidlprm  33391  mxidlprm  33403  qsdrngi  33428  1arithidom  33470  fldext2chn  33709  constrconj  33726  constrfin  33727  constrelextdg2  33728  zarcmplem  33862  afsval  34652  dffltz  42624  smfmullem3  46788