Theorem csbeq2dv 3162

Description: Formula-building deduction rule for class substitution. (Contributed by NM, 10-Nov-2005.) (Revised by Mario Carneiro, 1-Sep-2015.)

Hypothesis

Ref	Expression
csbeq2dv.1	⊢ (φ → B = C)

Assertion

Ref	Expression
csbeq2dv	⊢ (φ → [A / x]B = [A / x]C)

Distinct variable group:   φ,x

Allowed substitution hints:   A(x)   B(x)   C(x)

Proof of Theorem csbeq2dv

Step	Hyp	Ref	Expression
1		nfv 1619	. 2 ⊢ Ⅎxφ
2		csbeq2dv.1	. 2 ⊢ (φ → B = C)
3	1, 2	csbeq2d 3161	1 ⊢ (φ → [A / x]B = [A / 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:  csbeq2i  3163  fmpt2x  5731