Theorem iotabii 5105

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 5092	. 2 |- ( A. x ( ph <-> ps ) -> ( iota x ph ) = ( iota x ps ) )
2		iotabii.1	. 2 |- ( ph <-> ps )
3	1, 2	mpg 1427	1 |- ( iota x ph ) = ( iota x ps )

Syntax hints:   <-> wb 104   = wceq 1331   iotacio 5081

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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-rex 2420  df-uni 3732  df-iota 5083

This theorem is referenced by:  riotav  5728  cbvsum  11122  cbvprod  11320