Theorem simpr31 1259

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

Assertion

Ref	Expression
simpr31	⊢ ((𝜂 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑)

Proof of Theorem simpr31

Step	Hyp	Ref	Expression
1		simpr1 1190	. 2 ⊢ ((𝜂 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑)
2	1	3ad2antr3 1186	1 ⊢ ((𝜂 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 398   ∧ w3a 1083

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 209  df-an 399  df-3an 1085

This theorem is referenced by:  oppccatid  16983  subccatid  17110  fuccatid  17233  setccatid  17338  catccatid  17356  estrccatid  17376  xpccatid  17432  nllyidm  22091  utoptop  22837  cgr3tr4  33508  seglecgr12im  33566  paddasslem9  36958  cdlemd1  37328  cdlemf2  37692  cdlemk34  38040  dihmeetlem18N  38454  dihmeetlem19N  38455