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

Step	Hyp	Ref	Expression
1		sp 1859	. 2
2		hbn1 1838	. 2
3	1, 2	nsyl4 142	1

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