Theorem simpr1r 1233

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

Assertion

Ref	Expression
simpr1r	⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜓)

Proof of Theorem simpr1r

Step	Hyp	Ref	Expression
1		simprr 773	. 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	3ad2antr1 1190	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 399   ∧ w3a 1089

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 1091

This theorem is referenced by:  oppccatid  17223  subccatid  17352  setccatid  17590  catccatid  17612  estrccatid  17639  xpccatid  17695  gsmsymgreqlem1  18822  dmdprdsplit  19434  neitr  22077  neitx  22504  tx1stc  22547  utop3cls  23149  metustsym  23453  clwwlkccat  28073  3pthdlem1  28247  archiabllem1  31166  esumpcvgval  31758  esum2d  31773  poxp2  33527  ifscgr  34083  btwnconn1lem8  34133  btwnconn1lem11  34136  btwnconn1lem12  34137  segletr  34153  broutsideof3  34165  unbdqndv2  34428  lhp2lt  37752  cdlemf2  38313  cdlemn11pre  38961  stoweidlem60  43276  isthincd2  45992  mndtccatid  46045