Theorem iotasbcq 16403

Description: Theorem *14.272 in [WhiteheadRussell] p. 193.

Assertion

Ref	Expression
iotasbcq	|- (A.x(ph <-> ps) -> ([(iotaxph) / y]ch <-> [(iotaxps) / y]ch))

Proof of Theorem iotasbcq

Step	Hyp	Ref	Expression
1		iotabi 5094	. 2 |- (A.x(ph <-> ps) -> (iotaxph) = (iotaxps))
2		dfsbcq 2455	. 2 |- ((iotaxph) = (iotaxps) -> ([(iotaxph) / y]ch <-> [(iotaxps) / y]ch))
3	1, 2	syl 12	1 |- (A.x(ph <-> ps) -> ([(iotaxph) / y]ch <-> [(iotaxps) / y]ch))

Syntax hints:   -> wi 3   <-> wb 163  A.wal 1296   = wceq 1298  [wsbc 1534  iotacio 5087

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-sbc 2454  df-uni 3178  df-iota 5089

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