Theorem pm13.193 38612

Description: Theorem *13.193 in [WhiteheadRussell] p. 179. (Contributed by Andrew Salmon, 3-Jun-2011.)

Assertion

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

Proof of Theorem pm13.193

Step	Hyp	Ref	Expression
1		sbequ12 2111	. 2 |- ( x = y -> ( ph <-> [ y / x ] ph ) )
2	1	pm5.32ri 670	1 |- ( ( ph /\ x = y ) <-> ( [ y / x ] ph /\ x = y ) )

Syntax hints:   <-> wb 196   /\ wa 384   [wsb 1880

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-sb 1881

This theorem is referenced by: (None)