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Theorem ax4sp1 2251
Description: A special case of ax-4 2212 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
ax4sp1  |-  ( A. y  -.  x  =  x  ->  -.  x  =  x )

Proof of Theorem ax4sp1
StepHypRef Expression
1 equidqe 2250 . 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 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-6o 2214  ax-9o 2215
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