Metamath Proof Explorer


Theorem aecoms

Description: A commutation rule for identical variable specifiers. Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by NM, 10-May-1993) (New usage is discouraged.)

Ref Expression
Hypothesis aecoms.1
|- ( A. x x = y -> ph )
Assertion aecoms
|- ( A. y y = x -> ph )

Proof

Step Hyp Ref Expression
1 aecoms.1
 |-  ( A. x x = y -> ph )
2 aecom
 |-  ( A. y y = x <-> A. x x = y )
3 2 1 sylbi
 |-  ( A. y y = x -> ph )