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Theorem simpl12 1250
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
Assertion
Ref Expression
simpl12 ((((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜂) → 𝜓)

Proof of Theorem simpl12
StepHypRef Expression
1 simpl2 1193 . 2 (((𝜑𝜓𝜒) ∧ 𝜂) → 𝜓)
213ad2antl1 1186 1 ((((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜂) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395  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 207  df-an 396  df-3an 1089
This theorem is referenced by:  pythagtriplem4  16857  pmatcollpw1lem1  22780  pmatcollpw1  22782  mp2pm2mplem2  22813  nolt02o  27740  nogt01o  27741  brbtwn2  28920  ax5seg  28953  3vfriswmgr  30297  br8  35756  ifscgr  36045  seglecgr12im  36111  lkrshp  39106  atlatle  39321  cvlcvr1  39340  atbtwn  39448  3dimlem3  39463  3dimlem3OLDN  39464  1cvratex  39475  llnmlplnN  39541  4atlem3  39598  4atlem3a  39599  4atlem11  39611  4atlem12  39614  cdlemb  39796  paddasslem4  39825  paddasslem10  39831  pmodlem1  39848  llnexchb2lem  39870  arglem1N  40192  cdlemd4  40203  cdlemd  40209  cdleme16  40287  cdleme20  40326  cdleme21k  40340  cdleme22cN  40344  cdleme27N  40371  cdleme28c  40374  cdleme29ex  40376  cdleme32fva  40439  cdleme40n  40470  cdlemg15a  40657  cdlemg15  40658  cdlemg16ALTN  40660  cdlemg16z  40661  cdlemg20  40687  cdlemg22  40689  cdlemg29  40707  cdlemg38  40717  cdlemk33N  40911  cdlemk56  40973  fourierdlem77  46198
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