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Theorem albid 1579
Description: Formula-building rule for universal quantifier (deduction form). (Contributed by Mario Carneiro, 24-Sep-2016.)
Hypotheses
Ref Expression
albid.1 𝑥𝜑
albid.2 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
albid (𝜑 → (∀𝑥𝜓 ↔ ∀𝑥𝜒))

Proof of Theorem albid
StepHypRef Expression
1 albid.1 . . 3 𝑥𝜑
21nfri 1484 . 2 (𝜑 → ∀𝑥𝜑)
3 albid.2 . 2 (𝜑 → (𝜓𝜒))
42, 3albidh 1441 1 (𝜑 → (∀𝑥𝜓 ↔ ∀𝑥𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 104  wal 1314  wnf 1421
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-gen 1410  ax-4 1472
This theorem depends on definitions:  df-bi 116  df-nf 1422
This theorem is referenced by:  alexdc  1583  19.32dc  1642  eubid  1984  ralbida  2408  raleqf  2599  intab  3770  bdsepnft  13012  strcollnft  13109  sscoll2  13113
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