Theorem equidq 2254

Description: equid 1791 with universal quantifier without using ax-c5 2214 or ax-5 1704. (Contributed by NM, 13-Jan-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
equidq

Proof of Theorem equidq

Step	Hyp	Ref	Expression
1		equidqe 2252	. 2
2		ax10 2226	. . 3
3		hbequid 2239	. . . 4
4	3	con3i 135	. . 3
5	2, 4	alrimih 1642	. 2
6	1, 5	mt3 180	1

Syntax hints:  -.wn 3  A.wal 1393

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-7 1790  ax-c5 2214  ax-c4 2215  ax-c7 2216  ax-c10 2217  ax-c9 2221