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Theorem bnj1350 31228
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1350.1 (𝜒 → ∀𝑥𝜒)
Assertion
Ref Expression
bnj1350 ((𝜑𝜓𝜒) → ∀𝑥(𝜑𝜓𝜒))
Distinct variable groups:   𝜑,𝑥   𝜓,𝑥
Allowed substitution hint:   𝜒(𝑥)

Proof of Theorem bnj1350
StepHypRef Expression
1 ax-5 1990 . 2 (𝜑 → ∀𝑥𝜑)
2 ax-5 1990 . 2 (𝜓 → ∀𝑥𝜓)
3 bnj1350.1 . 2 (𝜒 → ∀𝑥𝜒)
41, 2, 3hb3an 2292 1 ((𝜑𝜓𝜒) → ∀𝑥(𝜑𝜓𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1070  wal 1628
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990  ax-6 2056  ax-7 2092  ax-10 2173  ax-12 2202
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 827  df-3an 1072  df-tru 1633  df-ex 1852  df-nf 1857
This theorem is referenced by:  bnj911  31334  bnj1093  31380
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