Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj1095 Structured version   Visualization version   GIF version

Theorem bnj1095 32061
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1095.1 (𝜑 ↔ ∀𝑥𝐴 𝜓)
Assertion
Ref Expression
bnj1095 (𝜑 → ∀𝑥𝜑)

Proof of Theorem bnj1095
StepHypRef Expression
1 bnj1095.1 . 2 (𝜑 ↔ ∀𝑥𝐴 𝜓)
2 hbra1 3207 . 2 (∀𝑥𝐴 𝜓 → ∀𝑥𝑥𝐴 𝜓)
31, 2hbxfrbi 1825 1 (𝜑 → ∀𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 208  wal 1535  wral 3125
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-10 2145  ax-12 2177
This theorem depends on definitions:  df-bi 209  df-or 844  df-ex 1781  df-nf 1785  df-ral 3130
This theorem is referenced by:  bnj1379  32110  bnj605  32187  bnj594  32192  bnj607  32196  bnj911  32212  bnj964  32223  bnj983  32231  bnj1093  32260  bnj1123  32266  bnj1145  32273  bnj1417  32321
  Copyright terms: Public domain W3C validator