Theorem simprl2 1220

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)

Assertion

Ref	Expression
simprl2	⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜓)

Proof of Theorem simprl2

Step	Hyp	Ref	Expression
1		simp2 1138	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜓)
2	1	ad2antrl 728	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 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:  poxp2  8168  poxp3  8175  icodiamlt  15474  issubc3  17894  clsconn  23438  txlly  23644  txnlly  23645  itg2add  25794  ftc1a  26078  nosupprefixmo  27745  noinfprefixmo  27746  nosupbnd2  27761  noinfbnd2  27776  mulsprop  28156  f1otrg  28879  ax5seglem6  28949  axcontlem9  28987  axcontlem10  28988  clwwlkf  30066  locfinref  33840  erdszelem7  35202  btwnconn1lem13  36100  dfsalgen2  46356  grtrimap  47915