Theorem 19.35ri 1796

Description: Inference associated with 19.35 1794. (Contributed by NM, 12-Mar-1993.)

Hypothesis

Ref	Expression
19.35ri.1	⊢ (∀𝑥𝜑 → ∃𝑥𝜓)

Assertion

Ref	Expression
19.35ri	⊢ ∃𝑥(𝜑 → 𝜓)

Proof of Theorem 19.35ri

Step	Hyp	Ref	Expression
1		19.35ri.1	. 2 ⊢ (∀𝑥𝜑 → ∃𝑥𝜓)
2		19.35 1794	. 2 ⊢ (∃𝑥(𝜑 → 𝜓) ↔ (∀𝑥𝜑 → ∃𝑥𝜓))
3	1, 2	mpbir 220	1 ⊢ ∃𝑥(𝜑 → 𝜓)

Syntax hints:   → wi 4  ∀wal 1473  ∃wex 1695

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728

This theorem depends on definitions:  df-bi 196  df-ex 1696

This theorem is referenced by:  qexmid  2051  axrep1  4700  axextnd  9292  axinfnd  9307  bj-axrep1  31976