Axiom ax-ia3 101

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

Assertion

Ref	Expression
ax-ia3	⊢ (𝜑 → (𝜓 → (𝜑 ∧ 𝜓)))

Detailed syntax breakdown of Axiom ax-ia3

Step	Hyp	Ref	Expression
1		wph	. 2 wff 𝜑
2		wps	. . 3 wff 𝜓
3	1, 2	wa 97	. . 3 wff (𝜑 ∧ 𝜓)
4	2, 3	wi 4	. 2 wff (𝜓 → (𝜑 ∧ 𝜓))
5	1, 4	wi 4	1 wff (𝜑 → (𝜓 → (𝜑 ∧ 𝜓)))

This axiom is referenced by:  ex  108  pm3.2  126  pm5.54dc  827  pclem6  1265  xoranor  1268  ax10oe  1678  2pwuninelg  5898  dmaddpq  6477  dmmulpq  6478  ltsopr  6694  ax1hfs  9898