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Theorem equidqe 2232
Description: equid 1731 with existential quantifier without using ax-c5 2194 or ax-5 1671. (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  |-  -.  A. y  -.  x  =  x

Proof of Theorem equidqe
StepHypRef Expression
1 ax6fromc10 2207 . 2  |-  -.  A. y  -.  y  =  x
2 ax-7 1730 . . . . 5  |-  ( y  =  x  ->  (
y  =  x  ->  x  =  x )
)
32pm2.43i 47 . . . 4  |-  ( y  =  x  ->  x  =  x )
43con3i 135 . . 3  |-  ( -.  x  =  x  ->  -.  y  =  x
)
54alimi 1605 . 2  |-  ( A. y  -.  x  =  x  ->  A. y  -.  y  =  x )
61, 5mto 176 1  |-  -.  A. y  -.  x  =  x
Colors of variables: wff setvar class
Syntax hints:   -. wn 3   A.wal 1368
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-7 1730  ax-c7 2196  ax-c10 2197
This theorem is referenced by:  axc5sp1  2233  equidq  2234
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