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Theorem ax4sp1 1426
Description: A special case of ax-4 1400 without using ax-4 1400 or ax-17 1419. (Contributed by NM, 13-Jan-2011.)
Assertion
Ref Expression
ax4sp1  |-  ( A. y  -.  x  =  x  ->  -.  x  =  x )

Proof of Theorem ax4sp1
StepHypRef Expression
1 equidqe 1425 . 2  |-  -.  A. y  -.  x  =  x
21pm2.21i 575 1  |-  ( A. y  -.  x  =  x  ->  -.  x  =  x )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1241
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1336  ax-gen 1338  ax-ie2 1383  ax-8 1395  ax-i9 1423
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249
This theorem is referenced by: (None)
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