Theorem orim12i 271

Description: Conjoin antecedents and consequents of two premises.

Hypotheses

Ref	Expression
orim12i.1	|- (ph -> ps)
orim12i.2	|- (ch -> th)

Assertion

Ref	Expression
orim12i	|- ((ph \/ ch) -> (ps \/ th))

Proof of Theorem orim12i

Step	Hyp	Ref	Expression
1		orim12i.1	. . . . 5 |- (ph -> ps)
2	1	con3i 90	. . . 4 |- (-. ps -> -. ph)
3		orim12i.2	. . . . 5 |- (ch -> th)
4	3	con3i 90	. . . 4 |- (-. th -> -. ch)
5	2, 4	anim12i 268	. . 3 |- ((-. ps /\ -. th) -> (-. ph /\ -. ch))
6	5	con3i 90	. 2 |- (-. (-. ph /\ -. ch) -> -. (-. ps /\ -. th))
7		oran 255	. 2 |- ((ph \/ ch) <-> -. (-. ph /\ -. ch))
8		oran 255	. 2 |- ((ps \/ th) <-> -. (-. ps /\ -. th))
9	6, 7, 8	3imtr4 192	1 |- ((ph \/ ch) -> (ps \/ th))

Syntax hints:  -. wn 1   -> wi 2   \/ wo 195   /\ wa 196

This theorem is referenced by:  orim1i 272  orim2i 273  pwssun 1917  funcnvuni 2706  nn0ge0i 4559  absor 4853

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198

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