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 738	1 ⊢ ((((((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 397

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 206  df-an 398

This theorem is referenced by:  catass  17630  2sqmo  26940  tgbtwnconn1  27826  legso  27850  miriso  27921  footexALT  27969  footex  27972  opphl  28005  lnopp2hpgb  28014  f1otrg  28122  2ndresdju  31874  cyc3genpm  32311  cyc3conja  32316  isprmidlc  32566  mxidlprm  32586  qsdrngi  32609  zarcmplem  32861  afsval  33683  dffltz  41376  smfmullem3  45509