Theorem biimp3a 1381

Description: Infer implication from a logical equivalence. Similar to biimpa 296. (Contributed by NM, 4-Sep-2005.)

Hypothesis

Ref	Expression
biimp3a.1	|- ( ( ph /\ ps ) -> ( ch <-> th ) )

Assertion

Ref	Expression
biimp3a	|- ( ( ph /\ ps /\ ch ) -> th )

Proof of Theorem biimp3a

Step	Hyp	Ref	Expression
1		biimp3a.1	. . 3 |- ( ( ph /\ ps ) -> ( ch <-> th ) )
2	1	biimpa 296	. 2 |- ( ( ( ph /\ ps ) /\ ch ) -> th )
3	2	3impa 1220	1 |- ( ( ph /\ ps /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   <-> wb 105   /\ 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:  nnawordex  6697  div2subap  9017  nn0addge1  9448  nn0addge2  9449  nn0sub2  9553  eluzp1p1  9782  uznn0sub  9788  iocssre  10188  icossre  10189  iccssre  10190  lincmb01cmp  10238  iccf1o  10239  fzosplitprm1  10480  subfzo0  10488  modfzo0difsn  10657  pfxpfx  11289  efltim  12260  fldivndvdslt  12499  prmdiv  12808  hashgcdlem  12811  vfermltl  12825  coprimeprodsq  12831  pythagtrip  12857  difsqpwdvds  12912  tgtop11  14802  sinq12gt0  15556  gausslemma2dlem1a  15789  s2elclwwlknon2  16289