Theorem simp-8r 790

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 739	1 ⊢ (((((((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 396

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 397

This theorem is referenced by:  2sqmo  26867  legso  27715  opphl  27870  f1otrg  27987  2ndresdju  31743  cyc3conja  32187  mxidlprm  32437  qtophaus  32647  esumcst  32892  dffltz  41158  smfmullem3  45282