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Theorem ralsns 3846
 Description: Substitution expressed in terms of quantification over a singleton. (Contributed by Mario Carneiro, 23-Apr-2015.)
Assertion
Ref Expression
ralsns
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem ralsns
StepHypRef Expression
1 sbc6g 3188 . 2
2 df-ral 2712 . . 3
3 elsn 3831 . . . . 5
43imbi1i 317 . . . 4
54albii 1576 . . 3
62, 5bitri 242 . 2
71, 6syl6rbbr 257 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178  wal 1550   wceq 1653   wcel 1726  wral 2707  wsbc 3163  csn 3816 This theorem is referenced by:  ralsng  3848  sbcsng  3867  rabrsn  3876  ac6sfi  7353  rexfiuz  12153  prmind2  13092 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-v 2960  df-sbc 3164  df-sn 3822
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