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Theorem hbaew5AUX7 29349
Description: Weak version of hbae 2005 not requiring ax-7 1745. (Contributed by NM, 30-Oct-2017.)
Assertion
Ref Expression
hbaew5AUX7  |-  ( A. u  u  =  v  ->  ( A. x  x  =  y  ->  A. z A. x  x  =  y ) )
Distinct variable group:    v, u

Proof of Theorem hbaew5AUX7
StepHypRef Expression
1 a16gNEW7 29250 1  |-  ( A. u  u  =  v  ->  ( A. x  x  =  y  ->  A. z A. x  x  =  y ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1546
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-11 1757  ax-12 1946  ax-7v 29148
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548  df-nf 1551
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