Theorem rmoimi 41176

Description: Restricted "at most one" is preserved through implication (note wff reversal). (Contributed by Alexander van der Vekens, 17-Jun-2017.)

Hypothesis

Ref	Expression
rmoimi.1	|- ( ph -> ps )

Assertion

Ref	Expression
rmoimi	|- ( E* x e. A ps -> E* x e. A ph )

Proof of Theorem rmoimi

Step	Hyp	Ref	Expression
1		rmoimi.1	. . 3 |- ( ph -> ps )
2	1	a1i 11	. 2 |- ( x e. A -> ( ph -> ps ) )
3	2	rmoimia 3408	1 |- ( E* x e. A ps -> E* x e. A ph )

Syntax hints:   -> wi 4   e. wcel 1990   E*wrmo 2915

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  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710  df-eu 2474  df-mo 2475  df-ral 2917  df-rmo 2920

This theorem is referenced by:  2rexreu  41185