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Theorem ax11wdemo 1697
 Description: Example of an application of ax11w 1695 that results in an instance of ax-11 1715 for a contrived formula with mixed free and bound variables, , in place of . The proof illustrates bound variable renaming with cbvalvw 1676 to obtain fresh variables to avoid distinct variable clashes. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 14-Apr-2017.)
Assertion
Ref Expression
ax11wdemo
Distinct variable group:   ,,

Proof of Theorem ax11wdemo
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 elequ1 1687 . . 3
2 elequ2 1689 . . . . 5
32cbvalvw 1676 . . . 4
43a1i 10 . . 3
5 elequ1 1687 . . . . . 6
65albidv 1611 . . . . 5
76cbvalvw 1676 . . . 4
8 elequ2 1689 . . . . . 6
98albidv 1611 . . . . 5
109albidv 1611 . . . 4
117, 10syl5bb 248 . . 3
121, 4, 113anbi123d 1252 . 2
13 elequ2 1689 . . 3
147a1i 10 . . 3
1513, 143anbi13d 1254 . 2
1612, 15ax11w 1695 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   w3a 934  wal 1527 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-13 1686  ax-14 1688 This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936  df-ex 1529
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