Theorem prlem2 929

Description: A specialized lemma for set theory (to derive the Axiom of Pairing). (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 13-May-2011.) (Proof shortened by Wolf Lammen, 9-Dec-2012.)

Assertion

Ref	Expression
prlem2	|- (((ph /\ ps) \/ (ch /\ th)) <-> ((ph \/ ch) /\ ((ph /\ ps) \/ (ch /\ th))))

Proof of Theorem prlem2

Step	Hyp	Ref	Expression
1		simpl 443	. . 3 |- ((ph /\ ps) -> ph)
2		simpl 443	. . 3 |- ((ch /\ th) -> ch)
3	1, 2	orim12i 502	. 2 |- (((ph /\ ps) \/ (ch /\ th)) -> (ph \/ ch))
4	3	pm4.71ri 614	1 |- (((ph /\ ps) \/ (ch /\ th)) <-> ((ph \/ ch) /\ ((ph /\ ps) \/ (ch /\ th))))

Syntax hints:   <-> 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)