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Theorem simp33l 1186
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp33l ((𝜏𝜂 ∧ (𝜒𝜃 ∧ (𝜑𝜓))) → 𝜑)

Proof of Theorem simp33l
StepHypRef Expression
1 simp3l 1087 . 2 ((𝜒𝜃 ∧ (𝜑𝜓)) → 𝜑)
213ad2ant3 1082 1 ((𝜏𝜂 ∧ (𝜒𝜃 ∧ (𝜑𝜓))) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  w3a 1036
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 386  df-3an 1038
This theorem is referenced by:  totprob  30270  cdleme19b  35072  cdleme19d  35074  cdleme19e  35075  cdleme20h  35084  cdleme20l2  35089  cdleme20m  35091  cdleme21d  35098  cdleme21e  35099  cdleme22e  35112  cdleme22f2  35115  cdleme22g  35116  cdleme26e  35127  cdleme28a  35138  cdleme28b  35139  cdleme37m  35230  cdleme39n  35234  cdlemeg46gfre  35300  cdlemg28a  35461  cdlemg28b  35471  cdlemk3  35601  cdlemk5a  35603  cdlemk6  35605  cdlemkuat  35634  cdlemkid2  35692
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