Theorem 19.8ad 1584

Description: If a wff is true, it is true for at least one instance. Deduction form of 19.8a 1583. (Contributed by DAW, 13-Feb-2017.)

Hypothesis

Ref	Expression
19.8ad.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
19.8ad	⊢ (𝜑 → ∃𝑥𝜓)

Proof of Theorem 19.8ad

Step	Hyp	Ref	Expression
1		19.8ad.1	. 2 ⊢ (𝜑 → 𝜓)
2		19.8a 1583	. 2 ⊢ (𝜓 → ∃𝑥𝜓)
3	1, 2	syl 14	1 ⊢ (𝜑 → ∃𝑥𝜓)

Syntax hints:   → wi 4  ∃wex 1485

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  suplocexprlemloc  7683  sgrpidmndm  12656