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Theorem bj-alequex 33225
Description: A fol lemma. Can be used to reduce the proof of spimt 1967 from 133 to 112 bytes. (Contributed by BJ, 6-Oct-2018.)
Assertion
Ref Expression
bj-alequex  |-  ( A. x ( x  =  y  ->  ph )  ->  E. x ph )

Proof of Theorem bj-alequex
StepHypRef Expression
1 ax6e 1964 . 2  |-  E. x  x  =  y
2 exim 1628 . 2  |-  ( A. x ( x  =  y  ->  ph )  -> 
( E. x  x  =  y  ->  E. x ph ) )
31, 2mpi 17 1  |-  ( A. x ( x  =  y  ->  ph )  ->  E. x ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1372   E.wex 1591
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-12 1798  ax-13 1961
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1592
This theorem is referenced by:  bj-spimt2  33226  bj-equsal1t  33351
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