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Theorem iotavalb 27645
 Description: Theorem *14.202 in [WhiteheadRussell] p. 189. A biconditional version of iotaval 5458. (Contributed by Andrew Salmon, 11-Jul-2011.)
Assertion
Ref Expression
iotavalb
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem iotavalb
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 iotaval 5458 . 2
2 iotasbc 27634 . . . 4
3 iotaexeu 27633 . . . . 5
4 eqsbc3 3206 . . . . 5
53, 4syl 16 . . . 4
62, 5bitr3d 248 . . 3
7 equequ2 1700 . . . . . . 7
87bibi2d 311 . . . . . 6
98albidv 1636 . . . . 5
109biimpac 474 . . . 4
1110exlimiv 1645 . . 3
126, 11syl6bir 222 . 2
131, 12impbid2 197 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wal 1550  wex 1551   wceq 1653   wcel 1727  weu 2287  cvv 2962  wsbc 3167  cio 5445 This theorem is referenced by:  iotavalsb  27648 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423 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-eu 2291  df-mo 2292  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-rex 2717  df-v 2964  df-sbc 3168  df-un 3311  df-sn 3844  df-pr 3845  df-uni 4040  df-iota 5447
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