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Theorem 19.21bbi 2224
Description: Inference removing two universal quantifiers. Version of 19.21bi 2223 with two quantifiers. (Contributed by NM, 20-Apr-1994.)
Hypothesis
Ref Expression
19.21bbi.1 (𝜑 → ∀𝑥𝑦𝜓)
Assertion
Ref Expression
19.21bbi (𝜑𝜓)

Proof of Theorem 19.21bbi
StepHypRef Expression
1 19.21bbi.1 . . 3 (𝜑 → ∀𝑥𝑦𝜓)
2119.21bi 2223 . 2 (𝜑 → ∀𝑦𝜓)
3219.21bi 2223 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1651
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-12 2213
This theorem depends on definitions:  df-bi 199  df-ex 1876
This theorem is referenced by:  2mo  2708  pocl  5241  funun  6147  fununi  6176  trclfvcotr  14090  pm14.24  39409
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