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  16991  subccatid  17118  fuccatid  17241  setccatid  17346  catccatid  17364  estrccatid  17384  xpccatid  17440  nllyidm  22099  utoptop  22845  cgr3tr4  33515  seglecgr12im  33573  paddasslem9  36966  cdlemd1  37336  cdlemf2  37700  cdlemk34  38048  dihmeetlem18N  38462  dihmeetlem19N  38463