Theorem nd5 1866

Description: A lemma for proving conditionless ZFC axioms. (Contributed by NM, 8-Jan-2002.)

Assertion

Ref	Expression
nd5	|- ( -. A. y y = x -> ( z = y -> A. x z = y ) )

Distinct variable group:   x, z

Proof of Theorem nd5

Step	Hyp	Ref	Expression
1		dveeq2 1863	. 2 |- ( -. A. x x = y -> ( z = y -> A. x z = y ) )
2	1	nalequcoms 1565	1 |- ( -. A. y y = x -> ( z = y -> A. x z = y ) )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1395   = wceq 1397

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 619  ax-in2 620  ax-io 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582

This theorem depends on definitions:  df-bi 117  df-nf 1509  df-sb 1811

This theorem is referenced by: (None)