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Theorem ax4sp1 2209
Description: A special case of ax-4 2170 without using ax-4 2170 or ax-17 1623. (Contributed by NM, 13-Jan-2011.) (Proof modification is discouraged.)
Assertion
Ref Expression
ax4sp1  |-  ( A. y  -.  x  =  x  ->  -.  x  =  x )

Proof of Theorem ax4sp1
StepHypRef Expression
1 equidqe 2208 . 2  |-  -.  A. y  -.  x  =  x
21pm2.21i 125 1  |-  ( A. y  -.  x  =  x  ->  -.  x  =  x )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1546
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-8 1682  ax-6o 2172  ax-9o 2173
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