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Theorem ax10w 1774
Description: Weak version of ax-10 1786 from which we can prove any ax-10 1786 instance not involving wff variables or bundling. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 9-Apr-2017.)
Hypothesis
Ref Expression
ax10w.1  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
Assertion
Ref Expression
ax10w  |-  ( -. 
A. x ph  ->  A. x  -.  A. x ph )
Distinct variable groups:    ph, y    ps, x    x, y
Allowed substitution hints:    ph( x)    ps( y)

Proof of Theorem ax10w
StepHypRef Expression
1 ax10w.1 . 2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
21hbn1w 1762 1  |-  ( -. 
A. x ph  ->  A. x  -.  A. x ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 184   A.wal 1377
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739
This theorem depends on definitions:  df-bi 185  df-ex 1597
This theorem is referenced by: (None)
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