Theorem hbaevg 1984

Description: Generalization of hbaev 1985, proved at no extra cost. Instance of aev2 1986. (Contributed by Wolf Lammen, 22-Mar-2021.) (Revised by BJ, 29-Mar-2021.)

Assertion

Ref	Expression
hbaevg	|- ( A. x x = y -> A. z A. t t = u )

Distinct variable groups:   x, y   u, t

Proof of Theorem hbaevg

Dummy variables v w are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		aevlem 1981	. 2 |- ( A. x x = y -> A. v v = w )
2		aevlem 1981	. . 3 |- ( A. v v = w -> A. t t = u )
3	2	alrimiv 1855	. 2 |- ( A. v v = w -> A. z A. t t = u )
4	1, 3	syl 17	1 |- ( A. x x = y -> A. z A. t t = u )

Syntax hints:   -> 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

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705

This theorem is referenced by:  hbaev  1985  aev2  1986