Theorem bj-ax6elem1 32651

Description: Lemma for bj-ax6e 32653. (Contributed by BJ, 22-Dec-2020.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-ax6elem1	|- ( -. A. x x = y -> ( y = z -> A. x y = z ) )

Distinct variable group:   x, z

Proof of Theorem bj-ax6elem1

Step	Hyp	Ref	Expression
1		axc9 2302	. 2 |- ( -. A. x x = y -> ( -. A. x x = z -> ( y = z -> A. x y = z ) ) )
2		axc16 2135	. 2 |- ( A. x x = z -> ( y = z -> A. x y = z ) )
3	1, 2	pm2.61d2 172	1 |- ( -. A. x x = y -> ( y = z -> A. x y = z ) )

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-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:  bj-ax6e  32653