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Theorem pw1sn 4165
 Description: Compute the unit power class of a singleton. (Contributed by SF, 22-Jan-2015.)
Hypothesis
Ref Expression
pw1sn.1
Assertion
Ref Expression
pw1sn 1

Proof of Theorem pw1sn
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 pw1sn.1 . . . 4
2 sneq 3744 . . . . 5
32eqeq2d 2364 . . . 4
41, 3rexsn 3768 . . 3
5 elpw1 4144 . . 3 1
6 elsn 3748 . . 3
74, 5, 63bitr4i 268 . 2 1
87eqriv 2350 1 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1642   wcel 1710  wrex 2615  cvv 2859  csn 3737  1 cpw1 4135 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334  ax-nin 4078  ax-sn 4087 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-rex 2620  df-v 2861  df-sbc 3047  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-ss 3259  df-nul 3551  df-pw 3724  df-sn 3741  df-1c 4136  df-pw1 4137 This theorem is referenced by:  pw1eqadj  4332  ncfinraise  4481  tfinsuc  4498  sfindbl  4530  tc1c  6165  ce0nn  6180  ce2  6192
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