Theorem simprl3 1220

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

Assertion

Ref	Expression
simprl3	⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜒)

Proof of Theorem simprl3

Step	Hyp	Ref	Expression
1		simp3 1138	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜒)
2	1	ad2antrl 726	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 396   ∧ 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 206  df-an 397  df-3an 1089

This theorem is referenced by:  poxp3  8138  ttrcltr  9713  pwfseqlem5  10660  icodiamlt  15386  issubc3  17803  pgpfac1lem5  19990  clsconn  23154  txlly  23360  txnlly  23361  itg2add  25501  ftc1a  25778  nosupprefixmo  27427  noinfprefixmo  27428  nosupbnd2  27443  noinfbnd2  27458  mulsprop  27813  f1otrg  28377  ax5seglem6  28447  axcontlem10  28486  numclwwlk5  29896  locfinref  33107  btwnouttr2  35286  btwnconn1lem13  35363  midofsegid  35368  outsideofeq  35394  ivthALT  35523  mpaaeu  42194  dfsalgen2  45356