Metamath Proof Explorer


Theorem eqeqan12rd

Description: A useful inference for substituting definitions into an equality. (Contributed by NM, 9-Aug-1994)

Ref Expression
Hypotheses eqeqan12rd.1 φ A = B
eqeqan12rd.2 ψ C = D
Assertion eqeqan12rd ψ φ A = C B = D

Proof

Step Hyp Ref Expression
1 eqeqan12rd.1 φ A = B
2 eqeqan12rd.2 ψ C = D
3 1 2 eqeqan12d φ ψ A = C B = D
4 3 ancoms ψ φ A = C B = D