Theorem exbi 1762

Description: Theorem 19.18 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.)

Assertion

Ref	Expression
exbi	⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∃𝑥𝜑 ↔ ∃𝑥𝜓))

Proof of Theorem exbi

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ ((𝜑 ↔ 𝜓) → (𝜑 ↔ 𝜓))
2	1	alexbii 1750	1 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∃𝑥𝜑 ↔ ∃𝑥𝜓))

Syntax hints:   → wi 4   ↔ wb 195  ∀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:  exbii  1764  exbidhOLD  1782  exintrbiOLD  1809  19.19  2084  bnj956  30101  bj-2exbi  31784  bj-3exbi  31785  bj-nfbi  31793  bj-nfbiit  32024  2exbi  37601  rexbidar  37671  onfrALTlem5VD  38143  onfrALTlem1VD  38148  csbxpgVD  38152  csbrngVD  38154  csbunigVD  38156  e2ebindVD  38170  e2ebindALT  38187