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Theorem sbcbii 3101
 Description: Formula-building inference rule for class substitution. (Contributed by NM, 11-Nov-2005.)
Hypothesis
Ref Expression
sbcbii.1 (φψ)
Assertion
Ref Expression
sbcbii ([̣A / xφ ↔ [̣A / xψ)

Proof of Theorem sbcbii
StepHypRef Expression
1 sbcbii.1 . . . 4 (φψ)
21a1i 10 . . 3 ( ⊤ → (φψ))
32sbcbidv 3100 . 2 ( ⊤ → ([̣A / xφ ↔ [̣A / xψ))
43trud 1323 1 ([̣A / xφ ↔ [̣A / xψ)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176   ⊤ wtru 1316  [̣wsbc 3046 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 This theorem is referenced by:  sbcbiiOLD  3102  eqsbc3r  3103  sbccomlem  3116  sbccom  3117  sbcrext  3119  sbcabel  3123  csbco  3145  sbcnel12g  3153  sbcne12g  3154  sbccsbg  3164  sbccsb2g  3165  csbnestgf  3184  csbabg  3197  sbcss  3660  inopab  4862  eqerlem  5960
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