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Theorem ax12w 1731
Description: Weak version (principal instance) of ax-12 1939. (Because  y and  z don't need to be distinct, this actually bundles the principal instance and the degenerate instance  ( -.  x  =  y  ->  ( y  =  y  ->  A. x
y  =  y ) ).) Uses only Tarski's FOL axiom schemes. The proof is trivial but is included to complete the set ax6w 1724, ax7w 1725, and ax11w 1728. (Contributed by NM, 10-Apr-2017.)
Assertion
Ref Expression
ax12w  |-  ( -.  x  =  y  -> 
( y  =  z  ->  A. x  y  =  z ) )
Distinct variable groups:    x, y    x, z

Proof of Theorem ax12w
StepHypRef Expression
1 a17d 1624 1  |-  ( -.  x  =  y  -> 
( y  =  z  ->  A. x  y  =  z ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1546
This theorem was proved from axioms:  ax-1 5  ax-mp 8  ax-17 1623
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