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Theorem equidq 2114
Description: equid 1644 with universal quantifier without using ax-4 2074 or ax-17 1603. (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 2112 . 2  |-  -.  A. y  -.  x  =  x
2 ax6 2086 . . 3  |-  ( -. 
A. y  x  =  x  ->  A. y  -.  A. y  x  =  x )
3 hbequid 2099 . . . 4  |-  ( x  =  x  ->  A. y  x  =  x )
43con3i 127 . . 3  |-  ( -. 
A. y  x  =  x  ->  -.  x  =  x )
52, 4alrimih 1552 . 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 1527
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-8 1643  ax-4 2074  ax-5o 2075  ax-6o 2076  ax-9o 2077  ax-12o 2081
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