Theorem exbid 1773

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 1762	. 2 |- (ph -> A.xph)
3		exbid.2	. 2 |- (ph -> (ps <-> ch))
4	2, 3	exbidh 1591	1 |- (ph -> (E.xps <-> E.xch))

This proof depends on syntax axioms:   -> wi 4   <-> wb 176  E.wex 1541   F/wnf 1544

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746

This proof depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545

This theorem is used by:  mobid  2238  rexbida  2630  rexeqf  2805  opabbid  4625  dfid3  4769  oprabbid  5564