Theorem ax4sp1 1543

Description: A special case of ax-4 1520 without using ax-4 1520 or ax-17 1536. (Contributed by NM, 13-Jan-2011.)

Assertion

Ref	Expression
ax4sp1	|- ( A. y -. x = x -> -. x = x )

Proof of Theorem ax4sp1

Step	Hyp	Ref	Expression
1		equidqe 1542	. 2 |- -. A. y -. x = x
2	1	pm2.21i 647	1 |- ( A. y -. x = x -> -. x = x )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1361

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-5 1457  ax-gen 1459  ax-ie2 1504  ax-8 1514  ax-i9 1540

This theorem depends on definitions:  df-bi 117  df-tru 1366  df-fal 1369

This theorem is referenced by: (None)