Theorem exbid 1614

Description: Formula-building rule for existential quantifier (deduction form). (Contributed by Mario Carneiro, 24-Sep-2016.)

Hypotheses

Ref	Expression
exbid.1	|- F/ x ph
exbid.2	|- ( ph -> ( ps <-> ch ) )

Assertion

Ref	Expression
exbid	|- ( ph -> ( E. x ps <-> E. x ch ) )

Proof of Theorem exbid

Step	Hyp	Ref	Expression
1		exbid.1	. . 3 |- F/ x ph
2	1	nfri 1517	. 2 |- ( ph -> A. x ph )
3		exbid.2	. 2 |- ( ph -> ( ps <-> ch ) )
4	2, 3	exbidh 1612	1 |- ( ph -> ( E. x ps <-> E. x ch ) )

Syntax hints:   -> wi 4   <-> wb 105   F/wnf 1458   E.wex 1490

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-5 1445  ax-gen 1447  ax-ie1 1491  ax-ie2 1492  ax-4 1508  ax-ial 1532

This theorem depends on definitions:  df-bi 117  df-nf 1459

This theorem is referenced by:  mobid  2059  rexbida  2470  rexbid2  2480  rexeqf  2667  opabbid  4063  repizf2  4157  oprabbid  5918