Theorem impac 421

Description: Importation with conjunction in consequent.

Hypothesis

Ref	Expression
impac.1	|- (ph -> (ps -> ch))

Assertion

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

Proof of Theorem impac

Step	Hyp	Ref	Expression
1		impac.1	. . 3 |- (ph -> (ps -> ch))
2	1	ancrd 321	. 2 |- (ph -> (ps -> (ch /\ ps)))
3	2	imp 375	1 |- ((ph /\ ps) -> (ch /\ ps))

Syntax hints:   -> wi 3   /\ wa 239

This theorem is referenced by:  imdistanri 490  zfrep6 4356  tfrlem5 4934  ac5b 5711  sqr2irr 7774  fsumsplit 8075  projlem27 10637  f1elima 15401  enf1f1o 15402

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 163  df-an 241

Copyright terms: Public domain