Theorem 19.35i 1879

Description: Inference associated with 19.35 1878. (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 1878	. 2 ⊢ (∃𝑥(𝜑 → 𝜓) ↔ (∀𝑥𝜑 → ∃𝑥𝜓))
3	1, 2	mpbi 232	1 ⊢ (∀𝑥𝜑 → ∃𝑥𝜓)

Syntax hints:   → wi 4  ∀wal 1535  ∃wex 1780

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810

This theorem depends on definitions:  df-bi 209  df-ex 1781

This theorem is referenced by:  spimehOLD  1975  19.2  1981  spimedv  2197  ax6e  2401  spimed  2406  equvini  2477  equviniOLD  2478  equvel  2479  axrep4  5195  zfcndrep  10036  bj-ax6elem2  34000  wl-exeq  34789  spd  44801