Theorem simpr33 1284

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 1215	. 2 ⊢ ((𝜂 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2antr3 1209	1 ⊢ ((𝜂 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

This proof depends on syntax axioms:   → wi 4   ∧ wa 401   ∧ w3a 1103

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  df-3an 1105

This theorem is used by:  oppccatid  17886  subccatid  18014  fuccatid  18140  setccatid  18252  catccatid  18274  estrccatid  18299  xpccatid  18355  nllyidm  23801  utoptop  24546  cgr3tr4  36797  paddasslem9  40865  cdlemd1  41235  cdlemf2  41599  cdlemk34  41947  dihmeetlem18N  42361  dihmeetlem19N  42362  ssccatid  50149  isthincd2  50514  mndtccatid  50664