Theorem 19.8ad 1644

Description: If a wff is true, it is true for at least one instance. Deduction form of 19.8a 1643. (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 1643	. 2 |- ( ps -> E. x ps )
3	1, 2	syl 14	1 |- ( ph -> E. x ps )

This proof depends on syntax axioms:   -> wi 4   E.wex 1545

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-4 1563

This proof depends on definitions:  df-bi 117

This theorem is used by:  rabsnif  3778  suplocexprlemloc  8088  sgrpidmndm  13733