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Theorem dfon2lem1 25412
 Description: Lemma for dfon2 25421. (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 4318 . 2
2 nfsbc1v 3182 . . . . 5
3 nfv 1630 . . . . 5
4 nfsbc1v 3182 . . . . 5
52, 3, 4nf3an 1850 . . . 4
6 vex 2961 . . . 4
7 sbceq1a 3173 . . . . 5
8 treq 4310 . . . . 5
9 sbceq1a 3173 . . . . 5
107, 8, 93anbi123d 1255 . . . 4
115, 6, 10elabf 3083 . . 3
1211simp2bi 974 . 2
131, 12mprg 2777 1
 Colors of variables: wff set class Syntax hints:   w3a 937   wcel 1726  cab 2424  wsbc 3163  cuni 4017   wtr 4304 This theorem is referenced by:  dfon2lem3  25414  dfon2lem7  25418 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-v 2960  df-sbc 3164  df-in 3329  df-ss 3336  df-uni 4018  df-iun 4097  df-tr 4305
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