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Theorem simp31r 1298
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 1199 . 2 (((𝜑𝜓) ∧ 𝜒𝜃) → 𝜓)
213ad2ant3 1136 1 ((𝜏𝜂 ∧ ((𝜑𝜓) ∧ 𝜒𝜃)) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395  w3a 1087
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 1089
This theorem is referenced by:  ps-2c  39530  cdlema1N  39793  cdlemednpq  40301  cdleme19e  40309  cdleme20h  40318  cdleme20j  40320  cdleme20l2  40323  cdleme20m  40325  cdleme22a  40342  cdleme22cN  40344  cdleme22f2  40349  cdleme26f2ALTN  40366  cdleme37m  40464  cdlemg12f  40650  cdlemg12g  40651  cdlemg12  40652  cdlemg28a  40695  cdlemg29  40707  cdlemg33a  40708  cdlemg36  40716  cdlemk16a  40858  cdlemk21-2N  40893  cdlemk54  40960  dihord10  41225
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