Theorem wl-equsalcom 33328

Description: This simple equivalence eases substitution of one expression for the other. (Contributed by Wolf Lammen, 1-Sep-2018.)

Assertion

Ref	Expression
wl-equsalcom	|- ( A. x ( x = y -> ph ) <-> A. x ( y = x -> ph ) )

Proof of Theorem wl-equsalcom

Step	Hyp	Ref	Expression
1		equcom 1945	. . 3 |- ( x = y <-> y = x )
2	1	imbi1i 339	. 2 |- ( ( x = y -> ph ) <-> ( y = x -> ph ) )
3	2	albii 1747	1 |- ( A. x ( x = y -> ph ) <-> A. x ( y = x -> ph ) )

Syntax hints:   -> wi 4   <-> wb 196   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-equsal1i  33329