Theorem simprl2 1218

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 1136	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜓)
2	1	ad2antrl 728	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1086

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 1088

This theorem is referenced by:  poxp2  8167  poxp3  8174  icodiamlt  15471  issubc3  17900  clsconn  23454  txlly  23660  txnlly  23661  itg2add  25809  ftc1a  26093  nosupprefixmo  27760  noinfprefixmo  27761  nosupbnd2  27776  noinfbnd2  27791  mulsprop  28171  f1otrg  28894  ax5seglem6  28964  axcontlem9  29002  axcontlem10  29003  clwwlkf  30076  locfinref  33802  erdszelem7  35182  btwnconn1lem13  36081  dfsalgen2  46297  grtrimap  47851