Theorem pm2.61ian 765

Description: Elimination of an antecedent. (Contributed by NM, 1-Jan-2005.)

Hypotheses

Ref	Expression
pm2.61ian.1	|- ((ph /\ ps) -> ch)
pm2.61ian.2	|- ((-. ph /\ ps) -> ch)

Assertion

Ref	Expression
pm2.61ian	|- (ps -> ch)

Proof of Theorem pm2.61ian

Step	Hyp	Ref	Expression
1		pm2.61ian.1	. . 3 |- ((ph /\ ps) -> ch)
2	1	ex 423	. 2 |- (ph -> (ps -> ch))
3		pm2.61ian.2	. . 3 |- ((-. ph /\ ps) -> ch)
4	3	ex 423	. 2 |- (-. ph -> (ps -> ch))
5	2, 4	pm2.61i 156	1 |- (ps -> ch)

Syntax hints:  -. wn 3   -> wi 4   /\ 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-an 360

This theorem is referenced by:  4cases  915  consensus  925  sbcom  2089  ax11indalem  2197  phi11lem1  4595  xpcan2  5058