Theorem imnani 412

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 411	. 2 |- ((ph -> -. ps) <-> -. (ph /\ ps))
3	1, 2	mpbir 200	1 |- (ph -> -. ps)

Syntax hints:  -. wn 3   -> wi 4   /\ wa 358

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 177  df-an 360

This theorem is referenced by:  mpto1  1533  eueq3  3012