Mathbox for Jonathan Ben-Naim < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj229 Structured version   Unicode version

Theorem bnj229 29156
 Description: Technical lemma for bnj517 29157. 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.)
Hypothesis
Ref Expression
bnj229.1
Assertion
Ref Expression
bnj229
Distinct variable groups:   ,,,   ,,,   ,,   ,,
Allowed substitution hints:   (,,,)   ()   (,)   ()   (,)

Proof of Theorem bnj229
StepHypRef Expression
1 bnj213 29154 . . 3
21bnj226 29002 . 2
3 bnj229.1 . . . . . . . 8
43bnj222 29155 . . . . . . 7
54bnj228 29003 . . . . . 6
65adantl 453 . . . . 5
7 eleq1 2495 . . . . . . 7
8 fveq2 5720 . . . . . . . 8
98eqeq1d 2443 . . . . . . 7
107, 9imbi12d 312 . . . . . 6
1110adantr 452 . . . . 5
126, 11mpbid 202 . . . 4
13123impb 1149 . . 3
1413impcom 420 . 2
152, 14bnj1262 29083 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   w3a 936   wceq 1652   wcel 1725  wral 2697   wss 3312  ciun 4085   csuc 4575  com 4837  cfv 5446   c-bnj14 28953 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 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-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  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-suc 4579  df-iota 5410  df-fv 5454  df-bnj14 28954
 Copyright terms: Public domain W3C validator