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Theorem 19.21bbi 2058
Description: Inference removing double quantifier. Version of 19.21bi 2057 with two quanditiers. (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 2057 . 2 (𝜑 → ∀𝑦𝜓)
3219.21bi 2057 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1478
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-12 2044
This theorem depends on definitions:  df-bi 197  df-ex 1702
This theorem is referenced by:  2mo  2550  pocl  5002  funun  5890  fununi  5922  trclfvcotr  13684  pm14.24  38112
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