Theorem simpr3r 1123

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

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

Proof of Theorem simpr3r

Step	Hyp	Ref	Expression
1		simp3r 1090	. 2 ⊢ ((𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	adantl 482	1 ⊢ ((𝜏 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 384   ∧ w3a 1037

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 197  df-an 386  df-3an 1039

This theorem is referenced by:  ax5seg  25818  segconeq  32117  ifscgr  32151  btwnconn1lem9  32202  btwnconn1lem11  32204  btwnconn1lem12  32205  lplnexllnN  34850  cdleme3b  35516  cdleme3c  35517  cdleme3e  35519  cdleme27a  35655