Theorem imnani 691

Description: Express implication in terms of conjunction. (Contributed by Mario Carneiro, 28-Sep-2015.)

Hypothesis

Ref	Expression
imnani.1	|- -. ( ph /\ ps )

Assertion

Ref	Expression
imnani	|- ( ph -> -. ps )

Proof of Theorem imnani

Step	Hyp	Ref	Expression
1		imnani.1	. 2 |- -. ( ph /\ ps )
2		imnan 690	. 2 |- ( ( ph -> -. ps ) <-> -. ( ph /\ ps ) )
3	1, 2	mpbir 146	1 |- ( ph -> -. ps )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  mptnan  1423  eueq3dc  2912  dtruex  4559  canth  5829  nntri2  6495  nndcel  6501