Theorem eqidd 2354

Description: Class identity law with antecedent. (Contributed by NM, 21-Aug-2008.)

Assertion

Ref	Expression
eqidd	⊢ (φ → A = A)

Proof of Theorem eqidd

Step	Hyp	Ref	Expression
1		eqid 2353	. 2 ⊢ A = A
2	1	a1i 10	1 ⊢ (φ → A = A)

Syntax hints:   → wi 4   = wceq 1642

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-cleq 2346

This theorem is referenced by:  nfabd2  2508  cbvraldva  2842  cbvrexdva  2843  iotanul  4355  fvopab4t  5386  eqfnov2  5591  mpteq1  5659  cbvmpt2  5680  erthi  5971  spaccl  6287