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Theorem wl-nfalv 31927
Description: If  x is not present in  ph, it is not free in  A. y ph. (Contributed by Wolf Lammen, 11-Jan-2020.)
Assertion
Ref Expression
wl-nfalv  |-  F/ x A. y ph
Distinct variable group:    ph, x
Allowed substitution hint:    ph( y)

Proof of Theorem wl-nfalv
StepHypRef Expression
1 ax-5 1766 . . 3  |-  ( ph  ->  A. x ph )
21hbal 1939 . 2  |-  ( A. y ph  ->  A. x A. y ph )
32nfi 1682 1  |-  F/ x A. y ph
Colors of variables: wff setvar class
Syntax hints:   A.wal 1450   F/wnf 1675
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-11 1937
This theorem depends on definitions:  df-bi 190  df-nf 1676
This theorem is referenced by: (None)
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