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Mirrors > Home > MPE Home > Th. List > Mathboxes > 2sbcrex | Structured version Visualization version Unicode version |
Description: Exchange an existential quantifier with two substitutions. (Contributed by Stefan O'Rear, 11-Oct-2014.) (Revised by NM, 24-Aug-2018.) |
Ref | Expression |
---|---|
2sbcrex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbcrex 3514 | . . 3 | |
2 | 1 | sbcbii 3491 | . 2 |
3 | sbcrex 3514 | . 2 | |
4 | 2, 3 | bitri 264 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wrex 2913 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-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-v 3202 df-sbc 3436 |
This theorem is referenced by: 2rexfrabdioph 37360 4rexfrabdioph 37362 |
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