Theorem sbceq1a 1944

Description: Equality theorem for class substitution.

Assertion

Ref	Expression
sbceq1a	|- (x = A -> (ph <-> [A / x]ph))

Proof of Theorem sbceq1a

Step	Hyp	Ref	Expression
1		dfsbcq 1943	. 2 |- (x = A -> ([x / x]ph <-> [A / x]ph))
2		sbid 1184	. 2 |- ([x / x]ph <-> ph)
3	1, 2	syl5bbr 534	1 |- (x = A -> (ph <-> [A / x]ph))

Syntax hints:   -> wi 3   <-> wb 146   = wceq 956  [wsbc 1170

This theorem is referenced by:  sbc5g 1954  sbc6g 1955  elrabsf 1963  sbcel1gv 1980  sbcel2gv 1981  sbcbrg 2662  reuuni4 2887  reuuniss 2889  reuuniss2 2891  sbcopeq1a 4111  dfopab2 4113  dfoprab3 4114  nn1suc 5939  uzindOLD 6208  nn0ind-raph 6214  fzrevralt 6519

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-sb 1172  df-cleq 1469  df-clel 1472  df-sbc 1942

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