Theorem pm13.193 16375

Description: Theorem *13.193 in [WhiteheadRussell] p. 179.

Assertion

Ref	Expression
pm13.193	|- ((ph /\ x = y) <-> ([y / x]ph /\ x = y))

Proof of Theorem pm13.193

Step	Hyp	Ref	Expression
1		sbequ12 1545	. 2 |- (x = y -> (ph <-> [y / x]ph))
2	1	pm5.32ri 708	1 |- ((ph /\ x = y) <-> ([y / x]ph /\ x = y))

Syntax hints:   <-> wb 163   /\ wa 240   = wceq 1298  [wsbc 1534

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-4 1319

This theorem depends on definitions:  df-bi 164  df-an 242  df-ex 1327  df-sb 1536

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