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Theorem simp33l 1296
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 1197 . 2 ((𝜒𝜃 ∧ (𝜑𝜓)) → 𝜑)
213ad2ant3 1131 1 ((𝜏𝜂 ∧ (𝜒𝜃 ∧ (𝜑𝜓))) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 398  w3a 1083
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 209  df-an 399  df-3an 1085
This theorem is referenced by:  totprob  31693  cdleme19b  37476  cdleme19d  37478  cdleme19e  37479  cdleme20h  37488  cdleme20l2  37493  cdleme20m  37495  cdleme21d  37502  cdleme21e  37503  cdleme22e  37516  cdleme22f2  37519  cdleme22g  37520  cdleme26e  37531  cdleme28a  37542  cdleme28b  37543  cdleme37m  37634  cdleme39n  37638  cdlemeg46gfre  37704  cdlemg28a  37865  cdlemg28b  37875  cdlemk3  38005  cdlemk5a  38007  cdlemk6  38009  cdlemkuat  38038  cdlemkid2  38096
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