Theorem iotabidv 5102

Description: Formula-building deduction rule for iota.

Hypothesis

Ref	Expression
iotabidv.1	|- (ph -> (ps <-> ch))

Assertion

Ref	Expression
iotabidv	|- (ph -> (iotaxps) = (iotaxch))

Distinct variable group:   ph,x

Proof of Theorem iotabidv

Step	Hyp	Ref	Expression
1		iotabidv.1	. . 3 |- (ph -> (ps <-> ch))
2	1	19.21aiv 1664	. 2 |- (ph -> A.x(ps <-> ch))
3		iotabi 5094	. 2 |- (A.x(ps <-> ch) -> (iotaxps) = (iotaxch))
4	2, 3	syl 12	1 |- (ph -> (iotaxps) = (iotaxch))

Syntax hints:   -> wi 3   <-> wb 163  A.wal 1296   = wceq 1298  iotacio 5087

This theorem is referenced by:  riotaeqdv 5561  riotabidv 5562  riotabidva 5575  grpidvalNEW 17117  grpinvfvalNEW 17125  grpinvvalNEW 17126  ringidval 17149

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 1304  ax-gen 1305  ax-8 1306  ax-9 1307  ax-10 1308  ax-11 1309  ax-12 1310  ax-17 1317  ax-4 1319  ax-5o 1321  ax-6o 1324  ax-9o 1481  ax-10o 1500  ax-16 1580  ax-11o 1588  ax-ext 1865

This theorem depends on definitions:  df-bi 164  df-or 241  df-an 242  df-ex 1327  df-sb 1536  df-clab 1872  df-cleq 1877  df-clel 1880  df-rex 2110  df-uni 3178  df-iota 5089

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