Theorem csbeq1d 3142

Description: Equality deduction for proper substitution into a class. (Contributed by NM, 3-Dec-2005.)

Hypothesis

Ref	Expression
csbeq1d.1	|- (ph -> A = B)

Assertion

Ref	Expression
csbeq1d	|- (ph -> [_A / x]_C = [_B / x]_C)

Proof of Theorem csbeq1d

Step	Hyp	Ref	Expression
1		csbeq1d.1	. 2 |- (ph -> A = B)
2		csbeq1 3139	. 2 |- (A = B -> [_A / x]_C = [_B / x]_C)
3	1, 2	syl 15	1 |- (ph -> [_A / x]_C = [_B / x]_C)

Syntax hints:   -> wi 4   = wceq 1642  [_csb 3136

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-sbc 3047  df-csb 3137

This theorem is referenced by:  csbidmg  3190  csbco3g  3193  fmpt2x  5730