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Theorem simp213 1315
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp213 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜁) → 𝜒)

Proof of Theorem simp213
StepHypRef Expression
1 simp13 1207 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜒)
213ad2ant2 1136 1 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜁) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1089
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 210  df-an 400  df-3an 1091
This theorem is referenced by:  cdleme27a  38118  cdlemk5u  38612  cdlemk6u  38613  cdlemk7u  38621  cdlemk11u  38622  cdlemk12u  38623  cdlemk7u-2N  38639  cdlemk11u-2N  38640  cdlemk12u-2N  38641  cdlemk20-2N  38643  cdlemk22  38644  cdlemk22-3  38652  cdlemk33N  38660  cdlemk53b  38707  cdlemk53  38708  cdlemk55a  38710  cdlemkyyN  38713  cdlemk43N  38714
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