Theorem ex-an 31056

Description: Example for df-an 402. Example by David A. Wheeler. (Contributed by Mario Carneiro, 9-May-2015.)

Assertion

Ref	Expression
ex-an	⊢ (2 = 2 ∧ 3 = 3)

Proof of Theorem ex-an

Step	Hyp	Ref	Expression
1		eqid 2763	. 2 ⊢ 2 = 2
2		eqid 2763	. 2 ⊢ 3 = 3
3	1, 2	pm3.2i 476	1 ⊢ (2 = 2 ∧ 3 = 3)

This proof depends on syntax axioms:   ∧ wa 401   = wceq 1570  2c2 12427  3c3 12428

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813  df-cleq 2755

This theorem is used by: (None)