Theorem 19.35ri 1865

Description: Inference associated with 19.35 1863. (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 1863	. 2 ⊢ (∃𝑥(𝜑 → 𝜓) ↔ (∀𝑥𝜑 → ∃𝑥𝜓))
3	1, 2	mpbir 232	1 ⊢ ∃𝑥(𝜑 → 𝜓)

Syntax hints:   → wi 4  ∀wal 1523  ∃wex 1765

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1781  ax-4 1795

This theorem depends on definitions:  df-bi 208  df-ex 1766

This theorem is referenced by:  qexmid  2158  axrep1  5089  axextnd  9866  axinfnd  9881