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Theorem dfon2lem1 30500
 Description: Lemma for dfon2 30509. (Contributed by Scott Fenton, 28-Feb-2011.)
Assertion
Ref Expression
dfon2lem1

Proof of Theorem dfon2lem1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 truni 4504 . 2
2 nfsbc1v 3275 . . . . 5
3 nfv 1769 . . . . 5
4 nfsbc1v 3275 . . . . 5
52, 3, 4nf3an 2033 . . . 4
6 vex 3034 . . . 4
7 sbceq1a 3266 . . . . 5
8 treq 4496 . . . . 5
9 sbceq1a 3266 . . . . 5
107, 8, 93anbi123d 1365 . . . 4
115, 6, 10elabf 3172 . . 3
1211simp2bi 1046 . 2
131, 12mprg 2770 1
 Colors of variables: wff setvar class Syntax hints:   w3a 1007   wcel 1904  cab 2457  wsbc 3255  cuni 4190   wtr 4490 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ral 2761  df-rex 2762  df-v 3033  df-sbc 3256  df-in 3397  df-ss 3404  df-uni 4191  df-iun 4271  df-tr 4491 This theorem is referenced by:  dfon2lem3  30502  dfon2lem7  30506
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