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Theorem a12stdy3 29750
Description: Part of a study related to ax12o 1887. The consequent introduces two new variables. There are no distinct variable restrictions. (Contributed by NM, 14-Jan-2008.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
a12stdy3  |-  ( A. z ( z  =  x  /\  x  =  y )  ->  A. v E. y  x  =  w )

Proof of Theorem a12stdy3
StepHypRef Expression
1 a12stdy2 29749 . 2  |-  ( A. z ( z  =  x  /\  x  =  y )  ->  A. y 
y  =  x )
2 hbae 1906 . 2  |-  ( A. y  y  =  x  ->  A. v A. y 
y  =  x )
3 a12stdy1 29748 . . 3  |-  ( A. y  y  =  x  ->  E. y  x  =  w )
43alimi 1549 . 2  |-  ( A. v A. y  y  =  x  ->  A. v E. y  x  =  w )
51, 2, 43syl 18 1  |-  ( A. z ( z  =  x  /\  x  =  y )  ->  A. v E. y  x  =  w )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   A.wal 1530   E.wex 1531
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-nf 1535
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