Theorem reximddv3 39343

Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Contributed by Glauco Siliprandi, 5-Feb-2022.)

Hypotheses

Ref	Expression
reximddv3.1	|- ( ( ( ph /\ x e. A ) /\ ps ) -> ch )
reximddv3.2	|- ( ph -> E. x e. A ps )

Assertion

Ref	Expression
reximddv3	|- ( ph -> E. x e. A ch )

Distinct variable group:   ph, x

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

Proof of Theorem reximddv3

Step	Hyp	Ref	Expression
1		reximddv3.1	. . 3 |- ( ( ( ph /\ x e. A ) /\ ps ) -> ch )
2	1	anasss 679	. 2 |- ( ( ph /\ ( x e. A /\ ps ) ) -> ch )
3		reximddv3.2	. 2 |- ( ph -> E. x e. A ps )
4	2, 3	reximddv 3018	1 |- ( ph -> E. x e. A ch )

Syntax hints:   -> wi 4   /\ wa 384   e. wcel 1990   E.wrex 2913

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-ral 2917  df-rex 2918

This theorem is referenced by:  climisp  39978  climrescn  39980  climxlim2lem  40071