Theorem iotabii 5356

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 5342	. 2 |- ( A. x ( ph <-> ps ) -> ( iota x ph ) = ( iota x ps ) )
2		iotabii.1	. 2 |- ( ph <-> ps )
3	1, 2	mpg 1504	1 |- ( iota x ph ) = ( iota x ps )

Syntax hints:   <-> wb 105   = wceq 1402   iotacio 5330

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 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This theorem depends on definitions:  df-bi 117  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-rex 2534  df-uni 3931  df-iota 5332

This theorem is referenced by:  riotav  6034  cbvsum  12104  cbvprod  12303