Theorem simprl2 1269

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 1132	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜓)
2	1	ad2antrl 766	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 383   ∧ w3a 1072

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 385  df-3an 1074

This theorem is referenced by:  icodiamlt  14394  issubc3  16731  clsconn  21456  txlly  21662  txnlly  21663  itg2add  23746  ftc1a  24020  f1otrg  25972  ax5seglem6  26035  axcontlem9  26073  axcontlem10  26074  clwwlkf  27198  locfinref  30239  erdszelem7  31508  noprefixmo  32176  nosupbnd2  32190  btwnconn1lem13  32534  dfsalgen2  41081