Theorem 19.35i 1955

Description: Inference associated with 19.35 1954. (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 1954	. 2 ⊢ (∃𝑥(𝜑 → 𝜓) ↔ (∀𝑥𝜑 → ∃𝑥𝜓))
3	1, 2	mpbi 220	1 ⊢ (∀𝑥𝜑 → ∃𝑥𝜓)

Syntax hints:   → wi 4  ∀wal 1630  ∃wex 1853

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886

This theorem depends on definitions:  df-bi 197  df-ex 1854

This theorem is referenced by:  19.2  2058  spimeh  2080  ax6e  2395  spimed  2400  equvini  2483  equvel  2484  euex  2631  axrep4  4927  zfcndrep  9648  bj-ax6elem2  32980  bj-spimedv  33047  bj-axrep4  33119  wl-exeq  33652  spd  42953