Theorem exbid 1595

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 1499	. 2 |- ( ph -> A. x ph )
3		exbid.2	. 2 |- ( ph -> ( ps <-> ch ) )
4	2, 3	exbidh 1593	1 |- ( ph -> ( E. x ps <-> E. x ch ) )

Syntax hints:   -> wi 4   <-> wb 104   F/wnf 1436   E.wex 1468

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-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-ial 1514

This theorem depends on definitions:  df-bi 116  df-nf 1437

This theorem is referenced by:  mobid  2032  rexbida  2430  rexeqf  2621  opabbid  3988  repizf2  4081  oprabbid  5817  sscoll2  13175