Theorem 3expib 1232

Description: Exportation from triple conjunction. (Contributed by NM, 19-May-2007.)

Hypothesis

Ref	Expression
3exp.1	|- ( ( ph /\ ps /\ ch ) -> th )

Assertion

Ref	Expression
3expib	|- ( ph -> ( ( ps /\ ch ) -> th ) )

Proof of Theorem 3expib

Step	Hyp	Ref	Expression
1		3exp.1	. . 3 |- ( ( ph /\ ps /\ ch ) -> th )
2	1	3exp 1228	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
3	2	impd 254	1 |- ( ph -> ( ( ps /\ ch ) -> th ) )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1004

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 1006

This theorem is referenced by:  3anidm12  1331  mob  2988  eqbrrdva  4900  funimaexglem  5413  fco  5500  f1oiso2  5968  caovimo  6216  smoel2  6469  nnaword  6679  3ecoptocl  6793  rex2dom  6996  sbthlemi10  7165  distrnq0  7679  addassnq0  7682  prcdnql  7704  prcunqu  7705  genpdisj  7743  cauappcvgprlemrnd  7870  caucvgprlemrnd  7893  caucvgprprlemrnd  7921  nn0n0n1ge2b  9559  fzind  9595  icoshft  10225  fzen  10278  seq3coll  11107  shftuz  11395  mulgcd  12605  algcvga  12641  lcmneg  12664  isnmgm  13461  gsummgmpropd  13495  issgrpd  13513  iscmnd  13903  unitmulclb  14147  rmodislmodlem  14383  rmodislmod  14384  blssps  15170  blss  15171  metcnp3  15254  sincosq1sgn  15569  sincosq2sgn  15570  sincosq3sgn  15571  sincosq4sgn  15572  iswlkg  16199