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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
StepHypRef 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 )
43con3i 135 . . 3  |-  ( -. 
A. y  x  =  x  ->  -.  x  =  x )
52, 4alrimih 1661 . 2  |-  ( -. 
A. y  x  =  x  ->  A. y  -.  x  =  x
)
61, 5mt3 180 1  |-  A. y  x  =  x
Colors of variables: wff setvar class
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)
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