Metamath Proof Explorer


Theorem pm13.13b

Description: Theorem *13.13 in WhiteheadRussell p. 178 with different variable substitution. (Contributed by Andrew Salmon, 3-Jun-2011)

Ref Expression
Assertion pm13.13b [˙A / x]˙ φ x = A φ

Proof

Step Hyp Ref Expression
1 sbceq1a x = A φ [˙A / x]˙ φ
2 1 biimparc [˙A / x]˙ φ x = A φ