Theorem wl-hbae1 33303

Description: This specialization of hbae 2315 does not depend on ax-11 2034. (Contributed by Wolf Lammen, 8-Aug-2021.)

Assertion

Ref	Expression
wl-hbae1	|- ( A. x x = y -> A. y A. x x = y )

Proof of Theorem wl-hbae1

Step	Hyp	Ref	Expression
1		axc11n 2307	. 2 |- ( A. x x = y -> A. y y = x )
2		axc11n 2307	. . 3 |- ( A. y y = x -> A. x x = y )
3	2	axc4i 2131	. 2 |- ( A. y y = x -> A. y A. x x = y )
4	1, 3	syl 17	1 |- ( A. x x = y -> A. y A. x x = y )

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  ax-10 2019  ax-12 2047  ax-13 2246

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

This theorem is referenced by: (None)