Theorem dveel2ALT 2269

Description: Alternate proof of dveel2 2112 using ax-c16 2223 instead of ax-5 1704. (Contributed by NM, 10-May-2008.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
dveel2ALT

Distinct variable group:   ,

Proof of Theorem dveel2ALT

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		ax5el 2267	. 2
2		ax5el 2267	. 2
3		elequ2 1823	. 2
4	1, 2, 3	dvelimh 2078	1

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

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-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-c14 2222  ax-c16 2223

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