Theorem simpr32 1261

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 1192	. 2 ⊢ ((𝜂 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓)
2	1	3ad2antr3 1187	1 ⊢ ((𝜂 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 399   ∧ w3a 1084

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 210  df-an 400  df-3an 1086

This theorem is referenced by:  oppccatid  16981  subccatid  17108  fuccatid  17231  setccatid  17336  catccatid  17354  estrccatid  17374  xpccatid  17430  nllyidm  22094  utoptop  22840  omndmul2  30763  cgr3tr4  33626  paddasslem9  37124  cdlemd1  37494  cdlemf2  37858  cdlemk34  38206  dihmeetlem18N  38620