Theorem axc15 2085

Description: Derivation of set.mm's original ax-c15 2220 from ax-c11n 2219 and the shorter ax-12 1854 that has replaced it.

Theorem ax12 2234 shows the reverse derivation of ax-12 1854 from ax-c15 2220.

Normally, axc15 2085 should be used rather than ax-c15 2220, except by theorems specifically studying the latter's properties. (Contributed by NM, 3-Feb-2007.)

Assertion

Ref	Expression
axc15

Proof of Theorem axc15

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		ax-12 1854	. 2
2	1	ax12a2 2084	1

Syntax hints:  -.wn 3  ->wi 4  A.wal 1393

This theorem is referenced by:  ax12b  2086  equs5  2092  ax12vALT  2171

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  ax-13 1999

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617