Theorem simpr32 1264

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

Assertion

Ref	Expression
simpr32	⊢ ((𝜂 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓)

Proof of Theorem simpr32

Step	Hyp	Ref	Expression
1		simpr2 1195	. 2 ⊢ ((𝜂 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓)
2	1	3ad2antr3 1190	1 ⊢ ((𝜂 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1087

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 207  df-an 396  df-3an 1089

This theorem is referenced by:  oppccatid  17779  subccatid  17910  fuccatid  18039  setccatid  18151  catccatid  18173  estrccatid  18200  xpccatid  18257  nllyidm  23518  utoptop  24264  omndmul2  33062  cgr3tr4  36016  paddasslem9  39785  cdlemd1  40155  cdlemf2  40519  cdlemk34  40867  dihmeetlem18N  41281  isthincd2  48705  mndtccatid  48760