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Theorem hbnae-x12 29732
Description: Experiment to study ax12o 1887. Weak version of hbnae 1908. Does not use sp 1728, ax9 1902, ax10 1897, or ax12o 1887 but allows ax9v 1645. (Contributed by NM, 7-Nov-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
hbnae-x12  |-  ( -. 
A. x  x  =  y  ->  A. y  -.  A. x  x  =  y )
Distinct variable group:    x, y

Proof of Theorem hbnae-x12
StepHypRef Expression
1 hbae-x12 29731 . 2  |-  ( A. x  x  =  y  ->  A. y A. x  x  =  y )
21hbn 1732 1  |-  ( -. 
A. x  x  =  y  ->  A. y  -.  A. x  x  =  y )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1530
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
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532
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