Theorem naecoms-o 2257

Description: A commutation rule for distinct variable specifiers. Version of naecoms 2053 using ax-c11 2218. (Contributed by NM, 2-Jan-2002.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
nalequcoms-o.1

Assertion

Ref	Expression
naecoms-o

Proof of Theorem naecoms-o

Step	Hyp	Ref	Expression
1		aecom-o 2230	. . 3
2		nalequcoms-o.1	. . 3
3	1, 2	nsyl4 142	. 2
4	3	con1i 129	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-c11 2218

This theorem depends on definitions:  df-bi 185  df-ex 1613