Theorem equidqe 2252

Description: equid 1791 with existential quantifier without using ax-c5 2214 or ax-5 1704. (Contributed by NM, 13-Jan-2011.) (Proof shortened by Wolf Lammen, 27-Feb-2014.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
equidqe

Proof of Theorem equidqe

Step	Hyp	Ref	Expression
1		ax6fromc10 2227	. 2
2		ax-7 1790	. . . . 5
3	2	pm2.43i 47	. . . 4
4	3	con3i 135	. . 3
5	4	alimi 1633	. 2
6	1, 5	mto 176	1

Syntax hints:  -.wn 3  A.wal 1393

This theorem is referenced by:  axc5sp1  2253  equidq  2254

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-c7 2216  ax-c10 2217