Theorem hbnae 1699

Description: All variables are effectively bound in a distinct variable specifier. Lemma L19 in [Megill] p. 446 (p. 14 of the preprint). (Contributed by NM, 5-Aug-1993.)

Assertion

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

Proof of Theorem hbnae

Step	Hyp	Ref	Expression
1		hbae 1696	. 2 |- ( A. x x = y -> A. z A. x x = y )
2	1	hbn 1632	1 |- ( -. A. x x = y -> A. z -. A. x x = y )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1329

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-fal 1337

This theorem is referenced by:  hbnaes  1701  equs5  1801  sbal2  1995