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Theorem simp33l 1301
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 1202 . 2 ((𝜒𝜃 ∧ (𝜑𝜓)) → 𝜑)
213ad2ant3 1136 1 ((𝜏𝜂 ∧ (𝜒𝜃 ∧ (𝜑𝜓))) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 397  w3a 1088
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 398  df-3an 1090
This theorem is referenced by:  totprob  33426  cdleme19b  39175  cdleme19d  39177  cdleme19e  39178  cdleme20h  39187  cdleme20l2  39192  cdleme20m  39194  cdleme21d  39201  cdleme21e  39202  cdleme22e  39215  cdleme22f2  39218  cdleme22g  39219  cdleme26e  39230  cdleme28a  39241  cdleme28b  39242  cdleme37m  39333  cdleme39n  39337  cdlemeg46gfre  39403  cdlemg28a  39564  cdlemg28b  39574  cdlemk3  39704  cdlemk5a  39706  cdlemk6  39708  cdlemkuat  39737  cdlemkid2  39795
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