Theorem simpr3r 1232

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

Assertion

Ref	Expression
simpr3r	⊢ ((𝜏 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜓)

Proof of Theorem simpr3r

Step	Hyp	Ref	Expression
1		simprr 772	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	3ad2antr3 1187	1 ⊢ ((𝜏 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 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:  ax5seg  26732  segconeq  33584  ifscgr  33618  btwnconn1lem9  33669  btwnconn1lem11  33671  btwnconn1lem12  33672  lplnexllnN  36860  cdleme3b  37525  cdleme3c  37526  cdleme3e  37528  cdleme27a  37663