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Theorem iotavalsb 26800
 Description: Theorem *14.242 in [WhiteheadRussell] p. 192. (Contributed by Andrew Salmon, 11-Jul-2011.)
Assertion
Ref Expression
iotavalsb
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   (,,)

Proof of Theorem iotavalsb
StepHypRef Expression
1 19.8a 1758 . 2
2 df-eu 2118 . . 3
3 iotavalb 26797 . . . 4
4 dfsbcq 2923 . . . . 5
54eqcoms 2256 . . . 4
63, 5syl6bi 221 . . 3
72, 6sylbir 206 . 2
81, 7mpcom 34 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178  wal 1532  wex 1537   wceq 1619  weu 2114  wsbc 2921  cio 6141 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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