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Theorem bnj1352 29945
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 1826 . 2 (𝜑 → ∀𝑥𝜑)
2 bnj1352.1 . 2 (𝜓 → ∀𝑥𝜓)
31, 2hban 2112 1 ((𝜑𝜓) → ∀𝑥(𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  wal 1472
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-10 2005  ax-12 2033
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700
This theorem is referenced by:  bnj594  30029  bnj1309  30137
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