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Theorem iotavalb 26797
 Description: Theorem *14.202 in [WhiteheadRussell] p. 189. A biconditional version of iotaval 6154. (Contributed by Andrew Salmon, 11-Jul-2011.)
Assertion
Ref Expression
iotavalb
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem iotavalb
StepHypRef Expression
1 iotaval 6154 . 2
2 iotasbc 26786 . . . 4
3 iotaexeu 26785 . . . . 5
4 eqsbc3 2960 . . . . 5
53, 4syl 17 . . . 4
62, 5bitr3d 248 . . 3
7 equequ2 1830 . . . . . . 7
87bibi2d 311 . . . . . 6
98albidv 2004 . . . . 5
109biimpac 474 . . . 4
1110exlimiv 2023 . . 3
126, 11syl6bir 222 . 2
131, 12impbid2 197 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wa 360  wal 1532  wex 1537   wceq 1619   wcel 1621  weu 2114  cvv 2727  wsbc 2921  cio 6141 This theorem is referenced by:  iotavalsb  26800 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-eu 2118  df-mo 2119  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-rex 2514  df-v 2729  df-sbc 2922  df-un 3083  df-sn 3550  df-pr 3551  df-uni 3728  df-iota 6143
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