Theorem ax4sp1 1514

Description: A special case of ax-4 1488 without using ax-4 1488 or ax-17 1507. (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 1513	. 2 |- -. A. y -. x = x
2	1	pm2.21i 636	1 |- ( A. y -. x = x -> -. x = x )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1330

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-5 1424  ax-gen 1426  ax-ie2 1471  ax-8 1483  ax-i9 1511

This theorem depends on definitions:  df-bi 116  df-tru 1335  df-fal 1338

This theorem is referenced by: (None)