Theorem simpr33 1264

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 1195	. 2 ⊢ ((𝜂 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2antr3 1189	1 ⊢ ((𝜂 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 396   ∧ 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 206  df-an 397  df-3an 1088

This theorem is referenced by:  oppccatid  17430  subccatid  17561  fuccatid  17687  setccatid  17799  catccatid  17821  estrccatid  17848  xpccatid  17905  nllyidm  22640  utoptop  23386  cgr3tr4  34354  paddasslem9  37842  cdlemd1  38212  cdlemf2  38576  cdlemk34  38924  dihmeetlem18N  39338  dihmeetlem19N  39339  isthincd2  46319  mndtccatid  46374