Theorem bj-exa1i 37260

Description: Add an antecedent in an existentially quantified formula. Inference associated with exa1 1871. (Contributed by BJ, 6-Oct-2018.)

Hypothesis

Ref	Expression
bj-exa1i.1	⊢ ∃𝑥𝜑

Assertion

Ref	Expression
bj-exa1i	⊢ ∃𝑥(𝜓 → 𝜑)

Proof of Theorem bj-exa1i

Step	Hyp	Ref	Expression
1		bj-exa1i.1	. 2 ⊢ ∃𝑥𝜑
2		exa1 1871	. 2 ⊢ (∃𝑥𝜑 → ∃𝑥(𝜓 → 𝜑))
3	1, 2	ax-mp 5	1 ⊢ ∃𝑥(𝜓 → 𝜑)

This proof depends on syntax axioms:   → wi 4  ∃wex 1812

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842

This proof depends on definitions:  df-bi 210  df-ex 1813

This theorem is used by: (None)