Theorem imp4c 617

Description: An importation inference. (Contributed by NM, 26-Apr-1994.)

Hypothesis

Ref	Expression
imp4.1	|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Assertion

Ref	Expression
imp4c	|- ( ph -> ( ( ( ps /\ ch ) /\ th ) -> ta ) )

Proof of Theorem imp4c

Step	Hyp	Ref	Expression
1		imp4.1	. . 3 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
2	1	impd 447	. 2 |- ( ph -> ( ( ps /\ ch ) -> ( th -> ta ) ) )
3	2	impd 447	1 |- ( ph -> ( ( ( ps /\ ch ) /\ th ) -> ta ) )

Syntax hints:   -> wi 4   /\ wa 384

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 197  df-an 386

This theorem is referenced by:  imp44  622  imp5g  626  omordi  7646  omwordri  7652  omass  7660  oewordri  7672  umgrclwwlksge2  26912  upgr4cycl4dv4e  27045  elspansn5  28433  atcvat3i  29255  mdsymlem5  29266  sumdmdlem  29277  cvrat4  34729  sprsymrelfolem2  41743