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Theorem simp31r 1296
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp31r ((𝜏𝜂 ∧ ((𝜑𝜓) ∧ 𝜒𝜃)) → 𝜓)

Proof of Theorem simp31r
StepHypRef Expression
1 simp1r 1197 . 2 (((𝜑𝜓) ∧ 𝜒𝜃) → 𝜓)
213ad2ant3 1134 1 ((𝜏𝜂 ∧ ((𝜑𝜓) ∧ 𝜒𝜃)) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395  w3a 1086
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 1088
This theorem is referenced by:  ps-2c  39511  cdlema1N  39774  cdlemednpq  40282  cdleme19e  40290  cdleme20h  40299  cdleme20j  40301  cdleme20l2  40304  cdleme20m  40306  cdleme22a  40323  cdleme22cN  40325  cdleme22f2  40330  cdleme26f2ALTN  40347  cdleme37m  40445  cdlemg12f  40631  cdlemg12g  40632  cdlemg12  40633  cdlemg28a  40676  cdlemg29  40688  cdlemg33a  40689  cdlemg36  40697  cdlemk16a  40839  cdlemk21-2N  40874  cdlemk54  40941  dihord10  41206
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