Theorem simp-9r 806

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

Assertion

Ref	Expression
simp-9r	⊢ ((((((((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) → 𝜓)

Proof of Theorem simp-9r

Step	Hyp	Ref	Expression
1		id 23	. 2 ⊢ (𝜓 → 𝜓)
2	1	ad9antlr 756	1 ⊢ ((((((((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) → 𝜓)

This proof depends on syntax axioms:   → wi 4   ∧ wa 401

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402

This theorem is used by:  legso  29095  miriso  29175  footexALT  29226  footex  29229  tgaaddcpbllem1  29382  cgraer  29410  cgrabasimass  29411  angmgmaddcpbl  29423  angmgmaddcl  29424  angmgmaddlid  29425  prlngmolem2  29464  f1otrg  29481  2ndresdju  33318  rloccring  33908  qsdrngi  34103  1arithidom  34153  constrfin  34461