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Theorem spnfw 1640
Description: Weak version of sp 1716. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 1-Aug-2017.) (Proof shortened by Wolf Lammen, 13-Aug-2017.)
Hypothesis
Ref Expression
spnfw.1  |-  ( -. 
ph  ->  A. x  -.  ph )
Assertion
Ref Expression
spnfw  |-  ( A. x ph  ->  ph )

Proof of Theorem spnfw
Dummy variable  y is distinct from all other variables.
StepHypRef Expression
1 spnfw.1 . 2  |-  ( -. 
ph  ->  A. x  -.  ph )
2 idd 21 . 2  |-  ( x  =  y  ->  ( ph  ->  ph ) )
31, 2spimw 1638 1  |-  ( A. x ph  ->  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1527
This theorem is referenced by:  19.8w  1659
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-9 1635
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529
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