Theorem hbnae 1769

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 1766	. 2 |- ( A. x x = y -> A. z A. x x = y )
2	1	hbn 1699	1 |- ( -. A. x x = y -> A. z -. A. x x = y )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1396

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-fal 1404

This theorem is referenced by:  hbnaes  1771  equs5  1877  sbal2  2073