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Theorem axc7 1861
 Description: Show that the original axiom ax-c7 2216 can be derived from ax-10 1837 and others. See ax10 2226 for the rederivation of ax-10 1837 from ax-c7 2216. Normally, axc7 1861 should be used rather than ax-c7 2216, except by theorems specifically studying the latter's properties. (Contributed by NM, 21-May-2008.)
Assertion
Ref Expression
axc7

Proof of Theorem axc7
StepHypRef Expression
1 sp 1859 . 2
2 hbn1 1838 . 2
31, 2nsyl4 142 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  A.wal 1393 This theorem is referenced by:  axc7e  1862  modal-b  1863  axc10  2004  hbntg  29238  axc5c4c711  31308  hbntal  33326  bj-axc10v  34277 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854 This theorem depends on definitions:  df-bi 185  df-ex 1613
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