Theorem iotabii 5182

Description: Formula-building deduction for iota. (Contributed by Mario Carneiro, 2-Oct-2015.)

Hypothesis

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

Assertion

Ref	Expression
iotabii	|- ( iota x ph ) = ( iota x ps )

Proof of Theorem iotabii

Step	Hyp	Ref	Expression
1		iotabi 5169	. 2 |- ( A. x ( ph <-> ps ) -> ( iota x ph ) = ( iota x ps ) )
2		iotabii.1	. 2 |- ( ph <-> ps )
3	1, 2	mpg 1444	1 |- ( iota x ph ) = ( iota x ps )

Syntax hints:   <-> wb 104   = wceq 1348   iotacio 5158

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-rex 2454  df-uni 3797  df-iota 5160

This theorem is referenced by:  riotav  5814  cbvsum  11323  cbvprod  11521