ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  r19.29vva Structured version   Unicode version

Theorem r19.29vva 2450
Description: A commonly used pattern based on r19.29 2444, version with two restricted quantifiers. (Contributed by Thierry Arnoux, 26-Nov-2017.)
Hypotheses
Ref Expression
r19.29vva.1
r19.29vva.2
Assertion
Ref Expression
r19.29vva
Distinct variable groups:   ,   ,,   ,,
Allowed substitution hints:   (,)   ()   (,)

Proof of Theorem r19.29vva
StepHypRef Expression
1 r19.29vva.1 . . . . . 6
21ex 108 . . . . 5
32ralrimiva 2386 . . . 4
43ralrimiva 2386 . . 3
5 r19.29vva.2 . . 3
64, 5r19.29d2r 2449 . 2
7 pm3.35 329 . . . . 5
87ancoms 255 . . . 4
98rexlimivw 2423 . . 3
109rexlimivw 2423 . 2
116, 10syl 14 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wcel 1390  wral 2300  wrex 2301
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-ral 2305  df-rex 2306
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator