Theorem iotabii 5317

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 5303	. 2 |- ( A. x ( ph <-> ps ) -> ( iota x ph ) = ( iota x ps ) )
2		iotabii.1	. 2 |- ( ph <-> ps )
3	1, 2	mpg 1500	1 |- ( iota x ph ) = ( iota x ps )

Syntax hints:   <-> wb 105   = wceq 1398   iotacio 5291

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2364  df-rex 2517  df-uni 3899  df-iota 5293

This theorem is referenced by:  riotav  5987  cbvsum  12000  cbvprod  12199