Mathbox for Jonathan Ben-Naim < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj1542 Structured version   Unicode version

Theorem bnj1542 29228
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1542.1
bnj1542.2
bnj1542.3
bnj1542.4
Assertion
Ref Expression
bnj1542
Distinct variable groups:   ,   ,   ,,
Allowed substitution hints:   (,)   ()   ()

Proof of Theorem bnj1542
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bnj1542.3 . . 3
2 bnj1542.1 . . . 4
3 bnj1542.2 . . . 4
4 eqfnfv 5827 . . . . . 6
54necon3abid 2634 . . . . 5
6 df-ne 2601 . . . . . . 7
76rexbii 2730 . . . . . 6
8 rexnal 2716 . . . . . 6
97, 8bitri 241 . . . . 5
105, 9syl6bbr 255 . . . 4
112, 3, 10syl2anc 643 . . 3
121, 11mpbid 202 . 2
13 nfv 1629 . . 3
14 bnj1542.4 . . . . . 6
1514nfcii 2563 . . . . 5
16 nfcv 2572 . . . . 5
1715, 16nffv 5735 . . . 4
18 nfcv 2572 . . . 4
1917, 18nfne 2695 . . 3
20 fveq2 5728 . . . 4
21 fveq2 5728 . . . 4
2220, 21neeq12d 2616 . . 3
2313, 19, 22cbvrex 2929 . 2
2412, 23sylibr 204 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wa 359  wal 1549   wceq 1652   wcel 1725   wne 2599  wral 2705  wrex 2706   wfn 5449  cfv 5454 This theorem is referenced by:  bnj1523  29440 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 2417  ax-sep 4330  ax-nul 4338  ax-pow 4377  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-csb 3252  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-mpt 4268  df-id 4498  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-rn 4889  df-res 4890  df-ima 4891  df-iota 5418  df-fun 5456  df-fn 5457  df-fv 5462
 Copyright terms: Public domain W3C validator