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Theorem fnwe2val 27124
 Description: Lemma for fnwe2 27128. Substitute variables. (Contributed by Stefan O'Rear, 19-Jan-2015.)
Hypotheses
Ref Expression
fnwe2.su
fnwe2.t
Assertion
Ref Expression
fnwe2val
Distinct variable groups:   ,,,,   ,,,,   ,,,,   ,,,,,   ,,
Allowed substitution hints:   ()   ()   (,,)   ()

Proof of Theorem fnwe2val
StepHypRef Expression
1 vex 2959 . 2
2 vex 2959 . 2
3 fveq2 5728 . . . 4
4 fveq2 5728 . . . 4
53, 4breqan12d 4227 . . 3
63, 4eqeqan12d 2451 . . . 4
7 simpl 444 . . . . 5
8 fvex 5742 . . . . . . . 8
9 nfcv 2572 . . . . . . . 8
10 fnwe2.su . . . . . . . 8
118, 9, 10csbief 3292 . . . . . . 7
123csbeq1d 3257 . . . . . . 7
1311, 12syl5eqr 2482 . . . . . 6
1413adantr 452 . . . . 5
15 simpr 448 . . . . 5
167, 14, 15breq123d 4226 . . . 4
176, 16anbi12d 692 . . 3
185, 17orbi12d 691 . 2
19 fnwe2.t . 2
201, 2, 18, 19braba 4472 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wo 358   wa 359   wceq 1652  csb 3251   class class class wbr 4212  copab 4265  cfv 5454 This theorem is referenced by:  fnwe2lem2  27126  fnwe2lem3  27127 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-csb 3252  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-opab 4267  df-iota 5418  df-fv 5462
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