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Theorem raldifsnb 4161
 Description: Restricted universal quantification on a class difference with a singleton in terms of an implication. (Contributed by Alexander van der Vekens, 26-Jan-2018.)
Assertion
Ref Expression
raldifsnb
Distinct variable group:   ,

Proof of Theorem raldifsnb
StepHypRef Expression
1 elsn 4043 . . . . . 6
2 nnel 2802 . . . . . 6
3 nne 2658 . . . . . 6
41, 2, 33bitr4ri 278 . . . . 5
54con4bii 297 . . . 4
65imbi1i 325 . . 3
76ralbii 2888 . 2
8 raldifb 3643 . 2
97, 8bitri 249 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  <->wb 184  =wceq 1395  e.wcel 1818  =/=wne 2652  e/wnel 2653  A.wral 2807  \cdif 3472  {csn 4029 This theorem is referenced by:  dff14b  6178 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-nel 2655  df-ral 2812  df-v 3111  df-dif 3478  df-sn 4030
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