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Theorem axextdist 24156
 Description: ax-ext 2264 with distinctors instead of distinct variable restrictions. (Contributed by Scott Fenton, 13-Dec-2010.)
Assertion
Ref Expression
axextdist

Proof of Theorem axextdist
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfnae 1896 . . . 4
2 nfnae 1896 . . . 4
31, 2nfan 1771 . . 3
4 nfcvd 2420 . . . . 5
5 nfcvf 2441 . . . . . 6
65adantr 451 . . . . 5
74, 6nfeld 2434 . . . 4
8 nfcvf 2441 . . . . . 6
98adantl 452 . . . . 5
104, 9nfeld 2434 . . . 4
117, 10nfbid 1762 . . 3
12 elequ1 1687 . . . . 5
13 elequ1 1687 . . . . 5
1412, 13bibi12d 312 . . . 4
1514a1i 10 . . 3
163, 11, 15cbvald 1948 . 2
17 axext3 2266 . 2
1816, 17syl6bir 220 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 176   wa 358  wal 1527   wceq 1623   wcel 1684  wnfc 2406 This theorem is referenced by:  axext4dist  24157 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  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-cleq 2276  df-clel 2279  df-nfc 2408
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