Theorem mpanr2 709

Description: An inference based on modus ponens.

Hypotheses

Ref	Expression
mpanr2.1	|- ch
mpanr2.2	|- ((ph /\ (ps /\ ch)) -> th)

Assertion

Ref	Expression
mpanr2	|- ((ph /\ ps) -> th)

Proof of Theorem mpanr2

Step	Hyp	Ref	Expression
1		mpanr2.1	. . 3 |- ch
2		mpanr2.2	. . . 4 |- ((ph /\ (ps /\ ch)) -> th)
3	2	ex 373	. . 3 |- (ph -> ((ps /\ ch) -> th))
4	1, 3	mpan2i 698	. 2 |- (ph -> (ps -> th))
5	4	imp 350	1 |- ((ph /\ ps) -> th)

Syntax hints:   -> wi 3   /\ wa 223

This theorem is referenced by:  pm54.43 4552  aceq6b 4722  prlem934b 5118  muleqaddt 5677  rimul 6683  isumcmpi 7158  opnneissb 7678  blssopn 7819  blnei 7831  va1cnlem 8292  blocnilem 8408  lnopmult 9830

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 147  df-an 225

Copyright terms: Public domain