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Theorem bnj554 29207
 Description: Technical lemma for bnj852 29229. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj554.19
bnj554.20
bnj554.21
bnj554.22
bnj554.23
bnj554.24
Assertion
Ref Expression
bnj554
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,,,,)   (,,,,)   (,,,,)   (,,,,)   (,,,,)   (,,,)   (,,,,)   (,,,,)

Proof of Theorem bnj554
StepHypRef Expression
1 bnj554.19 . . 3
21bnj1254 29118 . 2
3 bnj554.20 . . 3
43simp3bi 974 . 2
5 simpr 448 . . 3
6 bnj551 29047 . . 3
7 fveq2 5720 . . . 4
8 fveq2 5720 . . . . 5
9 iuneq1 4098 . . . . . 6
10 bnj554.24 . . . . . 6
11 bnj554.23 . . . . . 6
129, 10, 113eqtr4g 2492 . . . . 5
138, 12syl 16 . . . 4
147, 13eqeqan12d 2450 . . 3
155, 6, 14syl2anc 643 . 2
162, 4, 15syl2an 464 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   w3a 936   wceq 1652   wcel 1725  ciun 4085   csuc 4575  com 4837  cfv 5446   w-bnj17 28987   c-bnj14 28989 This theorem is referenced by:  bnj558  29210 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-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395  ax-un 4693  ax-reg 7552 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 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-iun 4087  df-br 4205  df-opab 4259  df-eprel 4486  df-fr 4533  df-suc 4579  df-iota 5410  df-fv 5454  df-bnj17 28988
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