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Theorem ax4sp1 2113
Description: A special case of ax-4 2074 without using ax-4 2074 or ax-17 1603. (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 2112 . 2  |-  -.  A. y  -.  x  =  x
21pm2.21i 123 1  |-  ( A. y  -.  x  =  x  ->  -.  x  =  x )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   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-6o 2076  ax-9o 2077
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