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Theorem bnj1351 32093
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1351.1 (𝜑 → ∀𝑥𝜑)
Assertion
Ref Expression
bnj1351 ((𝜑𝜓) → ∀𝑥(𝜑𝜓))
Distinct variable group:   𝜓,𝑥
Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem bnj1351
StepHypRef Expression
1 bnj1351.1 . 2 (𝜑 → ∀𝑥𝜑)
2 ax-5 1907 . 2 (𝜓 → ∀𝑥𝜓)
31, 2hban 2304 1 ((𝜑𝜓) → ∀𝑥(𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 398  wal 1531
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1907  ax-6 1966  ax-7 2011  ax-10 2141  ax-12 2173
This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1536  df-ex 1777  df-nf 1781
This theorem is referenced by:  bnj1373  32297  bnj1445  32311
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