Theorem hbnae 2317

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, 13-May-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 2315	. 2 |- ( A. x x = y -> A. z A. x x = y )
2	1	hbn 2146	1 |- ( -. A. x x = y -> A. z -. A. x x = y )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710

This theorem is referenced by:  hbnaes  2319  eujustALT  2473  bj-hbnaeb  32807  ax6e2nd  38774  ax6e2ndVD  39144  ax6e2ndeqVD  39145  ax6e2ndALT  39166  ax6e2ndeqALT  39167