Theorem wl-ax11-lem5 33366

Description: Lemma. (Contributed by Wolf Lammen, 30-Jun-2019.)

Assertion

Ref	Expression
wl-ax11-lem5	|- ( A. u u = y -> ( A. u [ u / y ] ph <-> A. y ph ) )

Proof of Theorem wl-ax11-lem5

Step	Hyp	Ref	Expression
1		sbequ12r 2112	. . 3 |- ( u = y -> ( [ u / y ] ph <-> ph ) )
2	1	sps 2055	. 2 |- ( A. u u = y -> ( [ u / y ] ph <-> ph ) )
3	2	dral1 2325	1 |- ( A. u u = y -> ( A. u [ u / y ] ph <-> A. y ph ) )

Syntax hints:   -> wi 4   <-> wb 196   A.wal 1481   [wsb 1880

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  df-sb 1881

This theorem is referenced by:  wl-ax11-lem6  33367