Axiom ax-ia3 107

Description: 'And' introduction. One of the axioms of propositional logic. (Contributed by Mario Carneiro, 31-Jan-2015.)

Assertion

Ref	Expression
ax-ia3	|- ( ph -> ( ps -> ( ph /\ ps ) ) )

Detailed syntax breakdown of Axiom ax-ia3

Step	Hyp	Ref	Expression
1		wph	. 2 wff ph
2		wps	. . 3 wff ps
3	1, 2	wa 103	. . 3 wff ( ph /\ ps )
4	2, 3	wi 4	. 2 wff ( ps -> ( ph /\ ps ) )
5	1, 4	wi 4	1 wff ( ph -> ( ps -> ( ph /\ ps ) ) )

This axiom is referenced by:  ex  114  pm3.2  138  pm5.54dc  903  pclem6  1352  xoranor  1355  ax10oe  1769  2pwuninelg  6180  dmaddpq  7187  dmmulpq  7188  ltsopr  7404  ax1hfs  13240