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 1137	. 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  8083  poxp3  8090  icodiamlt  15363  issubc3  17774  clsconn  23333  txlly  23539  txnlly  23540  itg2add  25676  ftc1a  25960  nosupprefixmo  27628  noinfprefixmo  27629  nosupbnd2  27644  noinfbnd2  27659  mulsprop  28056  f1otrg  28834  ax5seglem6  28897  axcontlem9  28935  axcontlem10  28936  clwwlkf  30009  locfinref  33807  erdszelem7  35169  btwnconn1lem13  36072  dfsalgen2  46323  grtrimap  47931  pgn4cyclex  48100