Mathbox for Jonathan Ben-Naim < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj124 Structured version   Unicode version

Theorem bnj124 33008
 Description: Technical lemma for bnj150 33013. 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.) (Proof shortened by Mario Carneiro, 22-Dec-2016.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj124.1
bnj124.2
bnj124.3
bnj124.4
bnj124.5
Assertion
Ref Expression
bnj124
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()   (,)   (,)   (,)   (,)   (,)   (,)   (,)

Proof of Theorem bnj124
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bnj124.4 . 2
2 bnj124.5 . . . 4
32sbcbii 3391 . . 3
4 bnj124.1 . . . . 5
54bnj95 33001 . . . 4
6 nfv 1683 . . . . 5
76sbc19.21g 3404 . . . 4
85, 7ax-mp 5 . . 3
9 fneq1 5667 . . . . . . . 8
10 fneq1 5667 . . . . . . . 8
119, 10sbcie2g 3365 . . . . . . 7
125, 11ax-mp 5 . . . . . 6
1312bicomi 202 . . . . 5
14 bnj124.2 . . . . 5
15 bnj124.3 . . . . 5
1613, 14, 15, 5bnj206 32866 . . . 4
1716imbi2i 312 . . 3
183, 8, 173bitri 271 . 2
191, 18bitri 249 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   w3a 973   wceq 1379   wcel 1767  cvv 3113  wsbc 3331  c0 3785  csn 4027  cop 4033   wfn 5581  c1o 7120   c-bnj14 32820   w-bnj15 32824 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4568  ax-nul 4576  ax-pr 4686 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-rab 2823  df-v 3115  df-sbc 3332  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034  df-br 4448  df-opab 4506  df-rel 5006  df-cnv 5007  df-co 5008  df-dm 5009  df-fun 5588  df-fn 5589 This theorem is referenced by:  bnj150  33013  bnj153  33017
 Copyright terms: Public domain W3C validator