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Theorem fnwe2val 29573
 Description: Lemma for fnwe2 29577. 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 3081 . 2
2 vex 3081 . 2
3 fveq2 5802 . . . 4
4 fveq2 5802 . . . 4
53, 4breqan12d 4418 . . 3
63, 4eqeqan12d 2477 . . . 4
7 simpl 457 . . . . 5
8 fvex 5812 . . . . . . . 8
9 nfcv 2616 . . . . . . . 8
10 fnwe2.su . . . . . . . 8
118, 9, 10csbief 3423 . . . . . . 7
123csbeq1d 3405 . . . . . . 7
1311, 12syl5eqr 2509 . . . . . 6
1413adantr 465 . . . . 5
15 simpr 461 . . . . 5
167, 14, 15breq123d 4417 . . . 4
176, 16anbi12d 710 . . 3
185, 17orbi12d 709 . 2
19 fnwe2.t . 2
201, 2, 18, 19braba 4717 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wo 368   wa 369   wceq 1370  csb 3398   class class class wbr 4403  copab 4460  cfv 5529 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432  ax-sep 4524  ax-nul 4532  ax-pr 4642 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2266  df-mo 2267  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-ral 2804  df-rex 2805  df-rab 2808  df-v 3080  df-sbc 3295  df-csb 3399  df-dif 3442  df-un 3444  df-in 3446  df-ss 3453  df-nul 3749  df-if 3903  df-sn 3989  df-pr 3991  df-op 3995  df-uni 4203  df-br 4404  df-opab 4462  df-iota 5492  df-fv 5537 This theorem is referenced by:  fnwe2lem2  29575  fnwe2lem3  29576
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