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Theorem equidq 2252
Description: equid 1688 with universal quantifier without using ax-4 2212 or ax-17 1626. (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 2250 . 2  |-  -.  A. y  -.  x  =  x
2 ax6 2224 . . 3  |-  ( -. 
A. y  x  =  x  ->  A. y  -.  A. y  x  =  x )
3 hbequid 2237 . . . 4  |-  ( x  =  x  ->  A. y  x  =  x )
43con3i 129 . . 3  |-  ( -. 
A. y  x  =  x  ->  -.  x  =  x )
52, 4alrimih 1574 . 2  |-  ( -. 
A. y  x  =  x  ->  A. y  -.  x  =  x
)
61, 5mt3 173 1  |-  A. y  x  =  x
Colors of variables: wff set class
Syntax hints:   -. wn 3   A.wal 1549
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-8 1687  ax-4 2212  ax-5o 2213  ax-6o 2214  ax-9o 2215  ax-12o 2219
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