Theorem dveeq1-o 2265

Description: Quantifier introduction when one pair of variables is distinct. Version of dveeq1 2044 using ax-c11 . (Contributed by NM, 2-Jan-2002.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
dveeq1-o

Distinct variable group:   ,

Proof of Theorem dveeq1-o

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		ax-5 1704	. 2
2		ax-5 1704	. 2
3		equequ1 1798	. 2
4	1, 2, 3	dvelimf-o 2259	1

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

This theorem is referenced by:  ax12inda2ALT  2276

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  ax-c5 2214  ax-c4 2215  ax-c7 2216  ax-c11 2218  ax-c9 2221

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