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Theorem opsqrlem3 23645
 Description: Lemma for opsqri . (Contributed by NM, 22-Aug-2006.) (New usage is discouraged.)
Hypotheses
Ref Expression
opsqrlem2.1
opsqrlem2.2
opsqrlem2.3
Assertion
Ref Expression
opsqrlem3
Distinct variable group:   ,,
Allowed substitution hints:   (,)   (,)   (,)   (,)

Proof of Theorem opsqrlem3
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 id 20 . . 3
21, 1coeq12d 5037 . . . . 5
32oveq2d 6097 . . . 4
43oveq2d 6097 . . 3
51, 4oveq12d 6099 . 2
6 eqidd 2437 . 2
7 opsqrlem2.2 . . 3
8 id 20 . . . . 5
98, 8coeq12d 5037 . . . . . . 7
109oveq2d 6097 . . . . . 6
1110oveq2d 6097 . . . . 5
128, 11oveq12d 6099 . . . 4
13 eqidd 2437 . . . 4
1412, 13cbvmpt2v 6152 . . 3
157, 14eqtri 2456 . 2
16 ovex 6106 . 2
175, 6, 15, 16ovmpt2 6209 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wcel 1725  csn 3814   cxp 4876   ccom 4882  (class class class)co 6081   cmpt2 6083  c1 8991   cdiv 9677  cn 10000  c2 10049   cseq 11323   chos 22441   chot 22442   chod 22443  ch0o 22446  cho 22453 This theorem is referenced by:  opsqrlem4  23646  opsqrlem5  23647 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-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-id 4498  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-iota 5418  df-fun 5456  df-fv 5462  df-ov 6084  df-oprab 6085  df-mpt2 6086
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