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Theorem axc11 2114
Description: Show that ax-c11 32365 can be derived from ax-c11n 32366 in the form of axc11n 2109. Normally, axc11 2114 should be used rather than ax-c11 32365, except by theorems specifically studying the latter's properties. (Contributed by NM, 16-May-2008.) (Proof shortened by Wolf Lammen, 21-Apr-2018.)
Assertion
Ref Expression
axc11  |-  ( A. x  x  =  y  ->  ( A. x ph  ->  A. y ph )
)

Proof of Theorem axc11
StepHypRef Expression
1 axc112 1997 . 2  |-  ( A. y  y  =  x  ->  ( A. x ph  ->  A. y ph )
)
21aecoms 2112 1  |-  ( A. x  x  =  y  ->  ( A. x ph  ->  A. y ph )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1435
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-12 1909  ax-13 2058
This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1658  df-nf 1662
This theorem is referenced by:  hbae  2115  axc16gOLD  2121  dral1  2127  dral1ALT  2128  nd1  8956  nd2  8957  bj-hbaeb2  31327  wl-aetr  31764  ax6e2eq  36831  ax6e2eqVD  37214  2sb5ndVD  37217  2sb5ndALT  37239
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