Theorem equsb1 2368

Description: Substitution applied to an atomic wff. (Contributed by NM, 10-May-1993.)

Assertion

Ref	Expression
equsb1	|- [ y / x ] x = y

Proof of Theorem equsb1

Step	Hyp	Ref	Expression
1		sb2 2352	. 2 |- ( A. x ( x = y -> x = y ) -> [ y / x ] x = y )
2		id 22	. 2 |- ( x = y -> x = y )
3	1, 2	mpg 1724	1 |- [ y / x ] x = y

Syntax hints:   -> wi 4   [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  ax-13 2246

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

This theorem is referenced by:  sbequ8ALT  2407  sbie  2408  pm13.183  3344  exss  4931  frege54cor1b  38188  sb5ALT  38731  sb5ALTVD  39149