Theorem axc16ALT 2105

Description: Alternate proof of axc16 1941, shorter but requiring ax-11 1842 and using df-sb 1740. (Contributed by NM, 17-May-2008.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
axc16ALT

Distinct variable group:   ,

Proof of Theorem axc16ALT

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		sbequ12 1992	. 2
2		ax-5 1704	. . 3
3	2	hbsb3 2103	. 2
4	1, 3	axc16i 2064	1

Syntax hints:  ->wi 4  A.wal 1393  [wsb 1739

This theorem is referenced by:  axc16gALT  2106

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-11 1842  ax-12 1854  ax-13 1999

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740