Theorem simpr33 1266

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)

Assertion

Ref	Expression
simpr33	⊢ ((𝜂 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

Proof of Theorem simpr33

Step	Hyp	Ref	Expression
1		simpr3 1197	. 2 ⊢ ((𝜂 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2antr3 1191	1 ⊢ ((𝜂 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1086

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  df-3an 1088

This theorem is referenced by:  oppccatid  17633  subccatid  17761  fuccatid  17887  setccatid  17999  catccatid  18021  estrccatid  18046  xpccatid  18102  nllyidm  23424  utoptop  24169  cgr3tr4  36168  paddasslem9  40000  cdlemd1  40370  cdlemf2  40734  cdlemk34  41082  dihmeetlem18N  41496  dihmeetlem19N  41497  ssccatid  49233  isthincd2  49598  mndtccatid  49748