Metamath Proof Explorer


Theorem axc5sp1

Description: A special case of ax-c5 without using ax-c5 or ax-5 . (Contributed by NM, 13-Jan-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion axc5sp1
|- ( A. y -. x = x -> -. x = x )

Proof

Step Hyp Ref Expression
1 equidqe
 |-  -. A. y -. x = x
2 1 pm2.21i
 |-  ( A. y -. x = x -> -. x = x )