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Theorem axc11 2058
Description: Show that ax-c11 2220 can be derived from ax-c11n 2221 in the form of axc11n 2053. Normally, axc11 2058 should be used rather than ax-c11 2220, 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 1942 . 2  |-  ( A. y  y  =  x  ->  ( A. x ph  ->  A. y ph )
)
21aecoms 2056 1  |-  ( A. x  x  =  y  ->  ( A. x ph  ->  A. y ph )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1396
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-12 1859  ax-13 2004
This theorem depends on definitions:  df-bi 185  df-an 369  df-ex 1618  df-nf 1622
This theorem is referenced by:  hbae  2059  axc16gOLD  2065  dral1  2071  dral1ALT  2072  nd1  8953  nd2  8954  wl-aetr  30226  ax6e2eq  33743  ax6e2eqVD  34127  2sb5ndVD  34130  2sb5ndALT  34152  bj-hbaeb2  34811
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