Theorem exbi 1877

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 23	. 2 ⊢ ((𝜑 ↔ 𝜓) → (𝜑 ↔ 𝜓))
2	1	alexbii 1863	1 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∃𝑥𝜑 ↔ ∃𝑥𝜓))

Syntax hints:   → wi 4   ↔ wb 209  ∀wal 1568  ∃wex 1809

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839

This theorem depends on definitions:  df-bi 210  df-ex 1810

This theorem is referenced by:  exbii  1878  nfbiit  1881  19.19  2265  eubi  2612  axpr  5400  elirrv  9560  bj-2exbi  37205  bj-3exbi  37206  bj-hbyfrbi  37217  2exbi  45073  rexbidar  45138  onfrALTlem1VD  45581  csbxpgVD  45585  csbrngVD  45587  csbunigVD  45589  e2ebindVD  45603  e2ebindALT  45620