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Theorem iota2 5109
 Description: The unique element such that . (Contributed by Jeff Madsen, 1-Jun-2011.) (Revised by Mario Carneiro, 23-Dec-2016.)
Hypothesis
Ref Expression
iota2.1
Assertion
Ref Expression
iota2
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem iota2
StepHypRef Expression
1 elex 2692 . 2
2 simpl 108 . . 3
3 simpr 109 . . 3
4 iota2.1 . . . 4
6 nfv 1508 . . . 4
7 nfeu1 2008 . . . 4
86, 7nfan 1544 . . 3
9 nfvd 1509 . . 3
10 nfcvd 2280 . . 3
112, 3, 5, 8, 9, 10iota2df 5107 . 2
121, 11sylan 281 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1331   wcel 1480  weu 1997  cvv 2681  cio 5081 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-eu 2000  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-rex 2420  df-v 2683  df-sbc 2905  df-un 3070  df-sn 3528  df-pr 3529  df-uni 3732  df-iota 5083 This theorem is referenced by: (None)
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