Theorem simpr33 1364

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 1253	. 2 ⊢ ((𝜂 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2antr3 1242	1 ⊢ ((𝜂 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 385   ∧ w3a 1108

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 199  df-an 386  df-3an 1110

This theorem is referenced by:  oppccatid  16693  subccatid  16820  fuccatid  16943  setccatid  17048  catccatid  17066  estrccatid  17086  xpccatid  17143  nllyidm  21621  utoptop  22366  cgr3tr4  32672  paddasslem9  35849  cdlemd1  36219  cdlemf2  36583  cdlemk34  36931  dihmeetlem18N  37345  dihmeetlem19N  37346