Theorem baibr 537

Description: Move conjunction outside of biconditional. (Contributed by NM, 11-Jul-1994.)

Hypothesis

Ref	Expression
baib.1	⊢ (𝜑 ↔ (𝜓 ∧ 𝜒))

Assertion

Ref	Expression
baibr	⊢ (𝜓 → (𝜒 ↔ 𝜑))

Proof of Theorem baibr

Step	Hyp	Ref	Expression
1		baib.1	. . 3 ⊢ (𝜑 ↔ (𝜓 ∧ 𝜒))
2	1	baib 536	. 2 ⊢ (𝜓 → (𝜑 ↔ 𝜒))
3	2	bicomd 222	1 ⊢ (𝜓 → (𝜒 ↔ 𝜑))

Syntax hints:   → wi 4   ↔ wb 205   ∧ wa 396

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

This theorem depends on definitions:  df-bi 206  df-an 397

This theorem is referenced by:  rbaibr  538  pm5.44  543  exmoeub  2574  ssnelpss  4110  brinxp  5752  copsex2ga  5805  canth  7358  riotaxfrd  7396  iscard  9966  kmlem14  10154  ltxrlt  11280  elioo5  13377  prmind2  16618  pcelnn  16799  isnirred  20226  isreg2  22872  comppfsc  23027  kqcldsat  23228  elmptrab  23322  itg2uba  25252  prmorcht  26671  adjeq  31175  lnopcnbd  31276  cvexchlem  31608  maprnin  31943  topfne  35227  ismblfin  36517  ftc1anclem5  36553  isdmn2  36911  cdlemefrs29pre00  39254  cdlemefrs29cpre1  39257  isdomn3  41931  elmapintab  42332  bits0ALTV  46333