Theorem wl-naev 33302

Description: If some set variables can assume different values, then any two distinct set variables cannot always be the same. (Contributed by Wolf Lammen, 10-Aug-2019.)

Assertion

Ref	Expression
wl-naev	|- ( -. A. x x = y -> -. A. u u = v )

Distinct variable group:   v, u

Proof of Theorem wl-naev

Step	Hyp	Ref	Expression
1		aev 1983	. 2 |- ( A. u u = v -> A. x x = y )
2	1	con3i 150	1 |- ( -. A. x x = y -> -. A. u u = v )

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

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

This theorem is referenced by:  wl-sbcom2d-lem2  33343  wl-sbal1  33346  wl-sbal2  33347  wl-ax11-lem3  33364