Theorem exbi 1948

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 1933	1 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∃𝑥𝜑 ↔ ∃𝑥𝜓))

Syntax hints:   → wi 4   ↔ wb 198  ∀wal 1656  ∃wex 1880

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910

This theorem depends on definitions:  df-bi 199  df-ex 1881

This theorem is referenced by:  exbii  1949  nfbiit  1952  19.19  2274  mobiOLDOLD  2615  eubi  2657  bj-2exbi  33128  bj-3exbi  33129  2exbi  39419  rexbidar  39488  onfrALTlem1VD  39944  csbxpgVD  39948  csbrngVD  39950  csbunigVD  39952  e2ebindVD  39966  e2ebindALT  39983