Theorem nd5 1818

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 1815	. 2 |- ( -. A. x x = y -> ( z = y -> A. x z = y ) )
2	1	nalequcoms 1517	1 |- ( -. A. y y = x -> ( z = y -> A. x z = y ) )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1351   = wceq 1353

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 614  ax-in2 615  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763

This theorem is referenced by: (None)