Theorem 19.8ad 42458

Description: If a wff is true, it is true for at least one instance. Deductive form of 19.8a 2052. (Contributed by DAW, 13-Feb-2017.)

Hypothesis

Ref	Expression
19.8ad.1	|- ( ph -> ps )

Assertion

Ref	Expression
19.8ad	|- ( ph -> E. x ps )

Proof of Theorem 19.8ad

Step	Hyp	Ref	Expression
1		19.8ad.1	. 2 |- ( ph -> ps )
2		19.8a 2052	. 2 |- ( ps -> E. x ps )
3	1, 2	syl 17	1 |- ( ph -> E. x ps )

Syntax hints:   -> wi 4   E.wex 1704

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-12 2047

This theorem depends on definitions:  df-bi 197  df-ex 1705

This theorem is referenced by: (None)