MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  equidqe Unicode version

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
StepHypRef Expression
1 ax6fromc10 2227 . 2
2 ax-7 1790 . . . . 5
32pm2.43i 47 . . . 4
43con3i 135 . . 3
54alimi 1633 . 2
61, 5mto 176 1
Colors of variables: wff setvar class
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
  Copyright terms: Public domain W3C validator