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Theorem simp321 1407
 Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp321 ((𝜂𝜁 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜑)

Proof of Theorem simp321
StepHypRef Expression
1 simp21 1248 . 2 ((𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) → 𝜑)
213ad2ant3 1129 1 ((𝜂𝜁 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜑)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ w3a 1071 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 197  df-an 383  df-3an 1073 This theorem is referenced by:  dalemcnes  35459  dalempnes  35460  dalemrot  35466  dath2  35546  cdleme18d  36105  cdleme20i  36127  cdleme20j  36128  cdleme20l2  36131  cdleme20l  36132  cdleme20m  36133  cdleme20  36134  cdleme21j  36146  cdleme22eALTN  36155  cdlemk16a  36666  cdlemk12u-2N  36700  cdlemk21-2N  36701  cdlemk22  36703  cdlemk31  36706  cdlemk32  36707  cdlemk11ta  36739  cdlemk11tc  36755
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