Theorem axc5sp1 34208

Description: A special case of ax-c5 34168 without using ax-c5 34168 or ax-5 1839. (Contributed by NM, 13-Jan-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

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

Proof of Theorem axc5sp1

Step	Hyp	Ref	Expression
1		equidqe 34207	. 2 |- -. A. y -. x = x
2	1	pm2.21i 116	1 |- ( A. y -. x = x -> -. x = x )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-c7 34170  ax-c10 34171

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705

This theorem is referenced by: (None)