Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj1352 Structured version   Visualization version   GIF version

Theorem bnj1352 31998
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1352.1 (𝜓 → ∀𝑥𝜓)
Assertion
Ref Expression
bnj1352 ((𝜑𝜓) → ∀𝑥(𝜑𝜓))
Distinct variable group:   𝜑,𝑥
Allowed substitution hint:   𝜓(𝑥)

Proof of Theorem bnj1352
StepHypRef Expression
1 ax-5 1902 . 2 (𝜑 → ∀𝑥𝜑)
2 bnj1352.1 . 2 (𝜓 → ∀𝑥𝜓)
31, 2hban 2299 1 ((𝜑𝜓) → ∀𝑥(𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  wal 1526
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-10 2136  ax-12 2167
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776
This theorem is referenced by:  bnj594  32083  bnj1309  32191
  Copyright terms: Public domain W3C validator