Theorem nabi1i 14141

Description: Constructor rule for -/\.

Hypotheses

Ref	Expression
nabi1i.1	|- (ph <-> ps)
nabi1i.2	|- (ps -/\ ch)

Assertion

Ref	Expression
nabi1i	|- (ph -/\ ch)

Proof of Theorem nabi1i

Step	Hyp	Ref	Expression
1		nabi1i.2	. 2 |- (ps -/\ ch)
2		nabi1i.1	. . . 4 |- (ph <-> ps)
3	2	bicomi 189	. . 3 |- (ps <-> ph)
4		nabi1 14139	. . 3 |- ((ps <-> ph) -> ((ps -/\ ch) <-> (ph -/\ ch)))
5	3, 4	ax-mp 7	. 2 |- ((ps -/\ ch) <-> (ph -/\ ch))
6	1, 5	mpbi 206	1 |- (ph -/\ ch)

Syntax hints:   <-> wb 163   -/\ wnand 1229

This theorem is referenced by:  nabi12i 14143

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 164  df-an 242  df-nand 1230

Copyright terms: Public domain