Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  19.21bbi Structured version   Visualization version   GIF version

Theorem 19.21bbi 2187
 Description: Inference removing two universal quantifiers. Version of 19.21bi 2186 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 2186 . 2 (𝜑 → ∀𝑦𝜓)
3219.21bi 2186 1 (𝜑𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1536 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-12 2175 This theorem depends on definitions:  df-bi 210  df-ex 1782 This theorem is referenced by:  2mo  2710  pocl  5448  funun  6375  fununi  6404  trclfvcotr  14377  acycgrcycl  32570  pm14.24  41223
 Copyright terms: Public domain W3C validator