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Theorem prlem1 928
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 214 . . . 4
32adantld 453 . . 3
4 prlem1.2 . . . . 5
54pm2.21d 98 . . . 4
65adantrd 454 . . 3
73, 6jaao 495 . 2
87ex 423 1
Colors of variables: wff setvar class
Syntax hints:   wn 3   wi 4   wb 176   wo 357   wa 358
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 177  df-or 359  df-an 360
This theorem is referenced by: (None)
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