Theorem prlem2

Description: A specialized lemma for set theory (to derive the Axiom of Pairing). (Contributed by NM, 21-Jun-1993) (Proof shortened by Andrew Salmon, 13-May-2011) (Proof shortened by Wolf Lammen, 9-Dec-2012)

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

Proof

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