Theorem simprl2 1217

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 1135	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜓)
2	1	ad2antrl 724	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1085

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 206  df-an 396  df-3an 1087

This theorem is referenced by:  icodiamlt  15075  issubc3  17480  clsconn  22489  txlly  22695  txnlly  22696  itg2add  24829  ftc1a  25106  f1otrg  27136  ax5seglem6  27205  axcontlem9  27243  axcontlem10  27244  clwwlkf  28312  locfinref  31693  erdszelem7  33059  poxp2  33717  nosupprefixmo  33830  noinfprefixmo  33831  nosupbnd2  33846  noinfbnd2  33861  btwnconn1lem13  34328  dfsalgen2  43770