Theorem equidq 31911

Description: equid 1813 with universal quantifier without using ax-c5 31871 or ax-5 1723. (Contributed by NM, 13-Jan-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
equidq	|- A. y x = x

Proof of Theorem equidq

Step	Hyp	Ref	Expression
1		equidqe 31909	. 2 |- -. A. y -. x = x
2		ax10 31883	. . 3 |- ( -. A. y x = x -> A. y -. A. y x = x )
3		hbequid 31896	. . . 4 |- ( x = x -> A. y x = x )
4	3	con3i 135	. . 3 |- ( -. A. y x = x -> -. x = x )
5	2, 4	alrimih 1661	. 2 |- ( -. A. y x = x -> A. y -. x = x )
6	1, 5	mt3 180	1 |- A. y x = x

Syntax hints:   -. wn 3   A.wal 1401

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1637  ax-4 1650  ax-7 1812  ax-c5 31871  ax-c4 31872  ax-c7 31873  ax-c10 31874  ax-c9 31878

This theorem is referenced by: (None)