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Theorem spnfwOLD 1658
Description: Weak version of sp 1716. Uses only Tarski's FOL axiom schemes. Obsolete version of spnfw 1640 as of 13-Aug-2017. (Contributed by NM, 1-Aug-2017.) (New usage is discouraged.)
Hypothesis
Ref Expression
spnfw.3  |-  ( -. 
ph  ->  A. x  -.  ph )
Assertion
Ref Expression
spnfwOLD  |-  ( A. x ph  ->  ph )

Proof of Theorem spnfwOLD
Dummy variable  y is distinct from all other variables.
StepHypRef Expression
1 spnfw.3 . 2  |-  ( -. 
ph  ->  A. x  -.  ph )
2 ax-17 1603 . 2  |-  ( A. x ph  ->  A. y A. x ph )
3 ax-17 1603 . 2  |-  ( -. 
ph  ->  A. y  -.  ph )
4 biidd 228 . 2  |-  ( x  =  y  ->  ( ph 
<-> 
ph ) )
51, 2, 3, 4spfw 1657 1  |-  ( A. x ph  ->  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   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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