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Theorem ax4vK 27907
Description: Version of ax-4 1692 when  x does not occur in  ph. This provides the other direction of ax-17 1628. Uses only Tarski's FOL axiom schemes (see description for equidK 27889). (Contributed by NM, 10-Apr-2017.)
Assertion
Ref Expression
ax4vK  |-  ( A. x ph  ->  ph )
Distinct variable group:    ph, x

Proof of Theorem ax4vK
StepHypRef Expression
1 biidd 230 . 2  |-  ( x  =  y  ->  ( ph 
<-> 
ph ) )
21ax4wK 27906 1  |-  ( A. x ph  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 6   A.wal 1532
This theorem is referenced by:  19.8vK  27908
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-gen 1536  ax-8 1623  ax-17 1628  ax-9v 1632
This theorem depends on definitions:  df-bi 179
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