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Theorem wl-ax11-lem10 31835
 Description: We now have prepared everything. The unwanted variable is just in one place left. pm2.61 174 can be used in conjunction with wl-ax11-lem9 31834 to eliminate the second antecedent. Missing is something along the lines of ax-6 1794, so we could remove the first antecedent. But the Metamath axioms cannot accomplish this. Such a rule must reside one abstraction level higher than all others: It says that a distinctor implies a distinct variable condition on its contained setvar. This is only needed if such conditions are required, as ax-11v does. The result of this study is for me, that you cannot introduce a setvar capturing this condition, and hope to eliminate it later. (Contributed by Wolf Lammen, 30-Jun-2019.)
Assertion
Ref Expression
wl-ax11-lem10
Distinct variable group:   ,
Allowed substitution hints:   (,,)

Proof of Theorem wl-ax11-lem10
StepHypRef Expression
1 wl-ax11-lem8 31833 . . . . 5
2 wl-ax11-lem6 31831 . . . . 5
31, 2bitr3d 258 . . . 4
43biimpd 210 . . 3
54ex 435 . 2
65aecoms 2107 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 370  wal 1435  wsb 1786 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-12 1905  ax-13 2053  ax-wl-11v 31825 This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1660  df-nf 1664  df-sb 1787 This theorem is referenced by: (None)
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