Theorem hbnae 1719

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 1716	. 2 |- ( A. x x = y -> A. z A. x x = y )
2	1	hbn 1652	1 |- ( -. A. x x = y -> A. z -. A. x x = y )

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

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 1445  ax-7 1446  ax-gen 1447  ax-ie2 1492  ax-8 1502  ax-10 1503  ax-11 1504  ax-i12 1505  ax-4 1508  ax-17 1524  ax-i9 1528  ax-ial 1532

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-fal 1359

This theorem is referenced by:  hbnaes  1721  equs5  1827  sbal2  2018