Metamath Proof Explorer


Theorem dveeq1-o16

Description: Version of dveeq1 using ax-c16 instead of ax-5 . (Contributed by NM, 29-Apr-2008) TODO: Recover proof from older set.mm to remove use of ax-5 . (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion dveeq1-o16
|- ( -. A. x x = y -> ( y = z -> A. x y = z ) )

Proof

Step Hyp Ref Expression
1 ax5eq
 |-  ( w = z -> A. x w = z )
2 ax5eq
 |-  ( y = z -> A. w y = z )
3 equequ1
 |-  ( w = y -> ( w = z <-> y = z ) )
4 1 2 3 dvelimh
 |-  ( -. A. x x = y -> ( y = z -> A. x y = z ) )