Theorem iotabii 5301

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 5287	. 2 |- ( A. x ( ph <-> ps ) -> ( iota x ph ) = ( iota x ps ) )
2		iotabii.1	. 2 |- ( ph <-> ps )
3	1, 2	mpg 1497	1 |- ( iota x ph ) = ( iota x ps )

Syntax hints:   <-> wb 105   = wceq 1395   iotacio 5275

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-rex 2514  df-uni 3888  df-iota 5277

This theorem is referenced by:  riotav  5959  cbvsum  11866  cbvprod  12064