Axiom ax-ia3 106

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 102	. . 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  113  pm3.2  137  pm5.54dc  860  pclem6  1305  xoranor  1308  ax10oe  1718  2pwuninelg  5921  dmaddpq  6569  dmmulpq  6570  ltsopr  6786  ax1hfs  10786