Theorem csbeq1d 3143

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

Hypothesis

Ref	Expression
csbeq1d.1	⊢ (φ → A = B)

Assertion

Ref	Expression
csbeq1d	⊢ (φ → [A / x]C = [B / x]C)

Proof of Theorem csbeq1d

Step	Hyp	Ref	Expression
1		csbeq1d.1	. 2 ⊢ (φ → A = B)
2		csbeq1 3140	. 2 ⊢ (A = B → [A / x]C = [B / x]C)
3	1, 2	syl 15	1 ⊢ (φ → [A / x]C = [B / x]C)

Syntax hints:   → wi 4   = wceq 1642  [csb 3137

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 3048  df-csb 3138

This theorem is referenced by:  csbidmg  3191  csbco3g  3194  fmpt2x  5731