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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  33457  cdleme19b  39223  cdleme19d  39225  cdleme19e  39226  cdleme20h  39235  cdleme20l2  39240  cdleme20m  39242  cdleme21d  39249  cdleme21e  39250  cdleme22e  39263  cdleme22f2  39266  cdleme22g  39267  cdleme26e  39278  cdleme28a  39289  cdleme28b  39290  cdleme37m  39381  cdleme39n  39385  cdlemeg46gfre  39451  cdlemg28a  39612  cdlemg28b  39622  cdlemk3  39752  cdlemk5a  39754  cdlemk6  39756  cdlemkuat  39785  cdlemkid2  39843
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