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Theorem bnj1352 31126
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 1952 . 2 (𝜑 → ∀𝑥𝜑)
2 bnj1352.1 . 2 (𝜓 → ∀𝑥𝜓)
31, 2hban 2239 1 ((𝜑𝜓) → ∀𝑥(𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  wal 1594
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1835  ax-4 1850  ax-5 1952  ax-6 2018  ax-7 2054  ax-10 2132  ax-12 2160
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1599  df-ex 1818  df-nf 1823
This theorem is referenced by:  bnj594  31210  bnj1309  31318
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