Theorem exbid 1504

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

Hypotheses

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

Assertion

Ref	Expression
exbid	|- (ph -> (E.xps <-> E.xch))

Proof of Theorem exbid

Step	Hyp	Ref	Expression
1		exbid.1	. . 3 |- F/xph
2	1	nfri 1409	. 2 |- (ph -> A.xph)
3		exbid.2	. 2 |- (ph -> (ps <-> ch))
4	2, 3	exbidh 1502	1 |- (ph -> (E.xps <-> E.xch))

Syntax hints:   -> wi 4   <-> wb 98   F/wnf 1346  E.wex 1378

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-ial 1424

This theorem depends on definitions:  df-bi 110  df-nf 1347

This theorem is referenced by:  mobid  1932  rexbida  2315  rexeqf  2496  opabbid  3813  repizf2  3906  oprabbid  5500  sscoll2  9418