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Theorem ax11wdemoK 27826
 Description: Example of an application of ax11wK 27824 that results in an instance of ax-11 1624 for a contrived formula with mixed free and bound variables, , in place of . The proof illustrates bound variable renaming with cbvalvK 27813 to obtain fresh variables to avoid distinct variable clashes. Uses only Tarski's predicate calculus axiom schemes i.e. does not use ax-6 1534, ax-7 1535, ax-11 1624, or ax-12 1633, and uses ax-9v 1632 instead of ax-9 1684. See the description in the comment of equidK 27792. (Contributed by NM, 14-Apr-2017.)
Assertion
Ref Expression
ax11wdemoK
Distinct variable group:   ,,

Proof of Theorem ax11wdemoK
StepHypRef Expression
1 elequ1K 27796 . . 3
2 elequ2K 27797 . . . . 5
32cbvalvK 27813 . . . 4
43a1i 12 . . 3
5 elequ1K 27796 . . . . . 6
65albidvK 27803 . . . . 5
76cbvalvK 27813 . . . 4
8 elequ2K 27797 . . . . . 6
98albidvK 27803 . . . . 5
109albidvK 27803 . . . 4
117, 10syl5bb 250 . . 3
121, 4, 113anbi123d 1257 . 2
13 elequ2K 27797 . . 3
14 biidd 230 . . 3
157a1i 12 . . 3
1613, 14, 153anbi123d 1257 . 2
1712, 16ax11wK 27824 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   w3a 939  wal 1532 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-gen 1536  ax-8 1623  ax-13 1625  ax-14 1626  ax-17 1628  ax-9v 1632 This theorem depends on definitions:  df-bi 179  df-an 362  df-3an 941
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