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Theorem equidq 2127
Description: equid 1662 with universal quantifier without using ax-4 2087 or ax-17 1606. (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 2125 . 2  |-  -.  A. y  -.  x  =  x
2 ax6 2099 . . 3  |-  ( -. 
A. y  x  =  x  ->  A. y  -.  A. y  x  =  x )
3 hbequid 2112 . . . 4  |-  ( x  =  x  ->  A. y  x  =  x )
43con3i 127 . . 3  |-  ( -. 
A. y  x  =  x  ->  -.  x  =  x )
52, 4alrimih 1555 . 2  |-  ( -. 
A. y  x  =  x  ->  A. y  -.  x  =  x
)
61, 5mt3 171 1  |-  A. y  x  =  x
Colors of variables: wff set class
Syntax hints:   -. wn 3   A.wal 1530
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-8 1661  ax-4 2087  ax-5o 2088  ax-6o 2089  ax-9o 2090  ax-12o 2094
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