Theorem 19.35i 1897

Description: Inference associated with 19.35 1896. (Contributed by NM, 21-Jun-1993.)

Hypothesis

Ref	Expression
19.35i.1	⊢ ∃𝑥(𝜑 → 𝜓)

Assertion

Ref	Expression
19.35i	⊢ (∀𝑥𝜑 → ∃𝑥𝜓)

Proof of Theorem 19.35i

Step	Hyp	Ref	Expression
1		19.35i.1	. 2 ⊢ ∃𝑥(𝜑 → 𝜓)
2		19.35 1896	. 2 ⊢ (∃𝑥(𝜑 → 𝜓) ↔ (∀𝑥𝜑 → ∃𝑥𝜓))
3	1, 2	mpbi 232	1 ⊢ (∀𝑥𝜑 → ∃𝑥𝜓)

Syntax hints:   → wi 4  ∀wal 1557  ∃wex 1798

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828

This theorem depends on definitions:  df-bi 209  df-ex 1799

This theorem is referenced by:  19.2  1995  spimedv  2231  ax6e  2413  spimed  2418  equvini  2485  equvel  2486  axrep4OLD  5233  zfcndrep  10569  bj-ax6elem2  37103  wl-exeq  38001  spd  50263