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Theorem fpwwe2lem1 8508
 Description: Lemma for fpwwe2 8520. (Contributed by Mario Carneiro, 15-May-2015.)
Hypothesis
Ref Expression
fpwwe2.1
Assertion
Ref Expression
fpwwe2lem1
Distinct variable groups:   ,,,,   ,,   ,,,,
Allowed substitution hints:   (,)

Proof of Theorem fpwwe2lem1
StepHypRef Expression
1 simpll 732 . . . . 5
2 vex 2961 . . . . . 6
32elpw 3807 . . . . 5
41, 3sylibr 205 . . . 4
5 simplr 733 . . . . . 6
6 xpss12 4983 . . . . . . 7
71, 1, 6syl2anc 644 . . . . . 6
85, 7sstrd 3360 . . . . 5
9 vex 2961 . . . . . 6
109elpw 3807 . . . . 5
118, 10sylibr 205 . . . 4
124, 11jca 520 . . 3
1312ssopab2i 4484 . 2
14 fpwwe2.1 . 2
15 df-xp 4886 . 2
1613, 14, 153sstr4i 3389 1
 Colors of variables: wff set class Syntax hints:   wa 360   wceq 1653   wcel 1726  wral 2707  wsbc 3163   cin 3321   wss 3322  cpw 3801  csn 3816  copab 4267   wwe 4542   cxp 4878  ccnv 4879  cima 4883  (class class class)co 6083 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-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-in 3329  df-ss 3336  df-pw 3803  df-opab 4269  df-xp 4886
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