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Theorem equsalOLD 1967
Description: Obsolete proof of equsal 1966 as of 5-Feb-2018. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 12-Aug-2011.) (Revised by Mario Carneiro, 3-Oct-2016.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
equsal.1  |-  F/ x ps
equsal.2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
Assertion
Ref Expression
equsalOLD  |-  ( A. x ( x  =  y  ->  ph )  <->  ps )

Proof of Theorem equsalOLD
StepHypRef Expression
1 equsal.2 . . . . 5  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
2 equsal.1 . . . . . 6  |-  F/ x ps
3219.3 1787 . . . . 5  |-  ( A. x ps  <->  ps )
41, 3syl6bbr 255 . . . 4  |-  ( x  =  y  ->  ( ph 
<-> 
A. x ps )
)
54pm5.74i 237 . . 3  |-  ( ( x  =  y  ->  ph )  <->  ( x  =  y  ->  A. x ps ) )
65albii 1572 . 2  |-  ( A. x ( x  =  y  ->  ph )  <->  A. x
( x  =  y  ->  A. x ps )
)
72nfri 1774 . . . . 5  |-  ( ps 
->  A. x ps )
87a1d 23 . . . 4  |-  ( ps 
->  ( x  =  y  ->  A. x ps )
)
92, 8alrimi 1777 . . 3  |-  ( ps 
->  A. x ( x  =  y  ->  A. x ps ) )
10 ax9o 1950 . . 3  |-  ( A. x ( x  =  y  ->  A. x ps )  ->  ps )
119, 10impbii 181 . 2  |-  ( ps  <->  A. x ( x  =  y  ->  A. x ps ) )
126, 11bitr4i 244 1  |-  ( A. x ( x  =  y  ->  ph )  <->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177   A.wal 1546   F/wnf 1550
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-11 1757  ax-12 1946
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548  df-nf 1551
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