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Mirrors > Home > MPE Home > Th. List > Mathboxes > sbexi | Structured version Visualization version Unicode version |
Description: Discard class substitution in an existential quantification when substituting the quantified variable, in inference form. (Contributed by Giovanni Mascellani, 27-May-2019.) |
Ref | Expression |
---|---|
sbexi.1 |
Ref | Expression |
---|---|
sbexi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbexi.1 | . 2 | |
2 | nfe1 2027 | . . 3 | |
3 | 2 | sbcgf 3501 | . 2 |
4 | 1, 3 | ax-mp 5 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wex 1704 wcel 1990 cvv 3200 wsbc 3435 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-v 3202 df-sbc 3436 |
This theorem is referenced by: (None) |
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