MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  prlem1 Unicode version

Theorem prlem1 962
Description: A specialized lemma for set theory (to derive the Axiom of Pairing). (Contributed by NM, 18-Oct-1995.) (Proof shortened by Andrew Salmon, 13-May-2011.) (Proof shortened by Wolf Lammen, 5-Jan-2013.)
Hypotheses
Ref Expression
prlem1.1
prlem1.2
Assertion
Ref Expression
prlem1

Proof of Theorem prlem1
StepHypRef Expression
1 prlem1.1 . . . . 5
21biimprd 223 . . . 4
32adantld 467 . . 3
4 prlem1.2 . . . . 5
54pm2.21d 106 . . . 4
65adantrd 468 . . 3
73, 6jaao 509 . 2
87ex 434 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  \/wo 368  /\wa 369
This theorem is referenced by:  zfpair  4689
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371
  Copyright terms: Public domain W3C validator