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Theorem bj-ax12 31311
Description: A weaker form of ax-12 1950 and ax12v2 1952, namely the generalization over  x of the latter. In this statement, all occurrences of  x are bound. (Contributed by BJ, 26-Dec-2020.)
Assertion
Ref Expression
bj-ax12  |-  A. x
( x  =  t  ->  ( ph  ->  A. x ( x  =  t  ->  ph ) ) )
Distinct variable group:    x, t
Allowed substitution hints:    ph( x, t)

Proof of Theorem bj-ax12
StepHypRef Expression
1 ax12v2 1952 . 2  |-  ( x  =  t  ->  ( ph  ->  A. x ( x  =  t  ->  ph )
) )
21ax-gen 1677 1  |-  A. x
( x  =  t  ->  ( ph  ->  A. x ( x  =  t  ->  ph ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1450
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-12 1950
This theorem depends on definitions:  df-bi 190  df-an 378  df-ex 1672
This theorem is referenced by:  bj-ax12ssb  31312  bj-sb56  31316
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