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Theorem spnfw 1854
Description: Weak version of sp 1947. 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 25 . 2  |-  ( x  =  y  ->  ( ph  ->  ph ) )
31, 2spimw 1852 1  |-  ( A. x ph  ->  ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1452
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-6 1815
This theorem depends on definitions:  df-bi 190  df-ex 1674
This theorem is referenced by:  spfalw  1855
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