Theorem biimp3a 1235

Description: Infer implication from a logical equivalence. Similar to biimpa 280. (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 280	. 2 |- ( ( ( ph /\ ps ) /\ ch ) -> th )
3	2	3impa 1099	1 |- ( ( ph /\ ps /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 97   <-> wb 98   /\ w3a 885

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-3an 887

This theorem is referenced by:  nnawordex  6101  nn0addge1  8228  nn0addge2  8229  nn0sub2  8314  eluzp1p1  8498  uznn0sub  8504  iocssre  8822  icossre  8823  iccssre  8824  lincmb01cmp  8871  iccf1o  8872  fzosplitprm1  9090  subfzo0  9097