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Theorem simpl33 1255
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
Assertion
Ref Expression
simpl33 (((𝜃𝜏 ∧ (𝜑𝜓𝜒)) ∧ 𝜂) → 𝜒)

Proof of Theorem simpl33
StepHypRef Expression
1 simpl3 1192 . 2 (((𝜑𝜓𝜒) ∧ 𝜂) → 𝜒)
213ad2antl3 1186 1 (((𝜃𝜏 ∧ (𝜑𝜓𝜒)) ∧ 𝜂) → 𝜒)
Colors of variables: wff setvar class
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:  nosupres  27767  noinfres  27782  ax5seglem3a  28960  ax5seg  28968  numclwwlk1lem2foa  30383  br8d  32630  br8  35736  cgrextend  35990  segconeq  35992  trisegint  36010  ifscgr  36026  cgrsub  36027  btwnxfr  36038  seglecgr12im  36092  segletr  36096  atbtwn  39429  4atlem10b  39588  4atlem11  39592  4atlem12  39595  2lplnj  39603  paddasslem4  39806  paddasslem7  39809  pmodlem1  39829  4atex2  40060  trlval3  40170  arglem1N  40173  cdleme0moN  40208  cdleme20  40307  cdleme21j  40319  cdleme28c  40355  cdleme38n  40447  cdlemg6c  40603  cdlemg6  40606  cdlemg7N  40609  cdlemg16  40640  cdlemg16ALTN  40641  cdlemg16zz  40643  cdlemg20  40668  cdlemg22  40670  cdlemg37  40672  cdlemg31d  40683  cdlemg29  40688  cdlemg33b  40690  cdlemg33  40694  cdlemg46  40718  cdlemk25-3  40887
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