Theorem rmobidva 2695

Description: Formula-building rule for restricted existential quantifier (deduction form). (Contributed by NM, 16-Jun-2017.)

Hypothesis

Ref	Expression
rmobidva.1	|- ( ( ph /\ x e. A ) -> ( ps <-> ch ) )

Assertion

Ref	Expression
rmobidva	|- ( ph -> ( E* x e. A ps <-> E* x e. A ch ) )

Distinct variable group:   ph, x

Allowed substitution hints:   ps( x)   ch( x)   A( x)

Proof of Theorem rmobidva

Step	Hyp	Ref	Expression
1		nfv 1552	. 2 |- F/ x ph
2		rmobidva.1	. 2 |- ( ( ph /\ x e. A ) -> ( ps <-> ch ) )
3	1, 2	rmobida 2694	1 |- ( ph -> ( E* x e. A ps <-> E* x e. A ch ) )

Syntax hints:   -> wi 4   /\ wa 104   <-> wb 105   e. wcel 2177   E*wrmo 2488

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 1471  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-4 1534  ax-17 1550  ax-ial 1558

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-eu 2058  df-mo 2059  df-rmo 2493

This theorem is referenced by:  rmobidv  2696