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Theorem simp31l 1294
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp31l ((𝜏𝜂 ∧ ((𝜑𝜓) ∧ 𝜒𝜃)) → 𝜑)

Proof of Theorem simp31l
StepHypRef Expression
1 simp1l 1195 . 2 (((𝜑𝜓) ∧ 𝜒𝜃) → 𝜑)
213ad2ant3 1133 1 ((𝜏𝜂 ∧ ((𝜑𝜓) ∧ 𝜒𝜃)) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 394  w3a 1085
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 395  df-3an 1087
This theorem is referenced by:  ps-2c  38702  cdlema1N  38965  trlval3  39361  cdleme12  39445  cdlemednpq  39473  cdleme19d  39480  cdleme19e  39481  cdleme20f  39488  cdleme20h  39490  cdleme20l2  39495  cdleme20l  39496  cdleme20m  39497  cdleme21j  39510  cdleme22a  39514  cdleme22cN  39516  cdleme22f2  39521  cdleme32b  39616  cdlemg12f  39822  cdlemg12g  39823  cdlemg12  39824  cdlemg28a  39867  cdlemg31b0N  39868  cdlemg29  39879  cdlemg33a  39880  cdlemg36  39888  cdlemg42  39903  cdlemk16a  40030  cdlemk21-2N  40065  cdlemk32  40071  cdlemkid2  40098  cdlemk54  40132  cdlemk55a  40133  dihord10  40397
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