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Theorem ax6w 1691
Description: Weak version of ax-6 1703 from which we can prove any ax-6 1703 instance not involving wff variables or bundling. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 9-Apr-2017.)
Hypothesis
Ref Expression
ax6w.1  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
Assertion
Ref Expression
ax6w  |-  ( -. 
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 ax6w
StepHypRef Expression
1 ax6w.1 . 2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
21hbn1w 1680 1  |-  ( -. 
A. x ph  ->  A. x  -.  A. x ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176   A.wal 1527
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529
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