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Theorem ax11dgen 1708
Description: Degenerate instance of ax-11 1727 where bundled variables  x and  y have a common substitution. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 13-Apr-2017.)
Assertion
Ref Expression
ax11dgen  |-  ( x  =  x  ->  ( A. x ph  ->  A. x
( x  =  x  ->  ph ) ) )

Proof of Theorem ax11dgen
StepHypRef Expression
1 ax-1 5 . . 3  |-  ( ph  ->  ( x  =  x  ->  ph ) )
21alimi 1549 . 2  |-  ( A. x ph  ->  A. x
( x  =  x  ->  ph ) )
32a1i 10 1  |-  ( x  =  x  ->  ( A. x ph  ->  A. x
( x  =  x  ->  ph ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1530
This theorem was proved from axioms:  ax-1 5  ax-mp 8  ax-gen 1536  ax-5 1547
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