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Mirrors > Home > MPE Home > Th. List > r19.37 | Structured version Visualization version Unicode version |
Description: Restricted quantifier version of one direction of 19.37 2100. (The other direction does not hold when is empty.) (Contributed by FL, 13-May-2012.) (Revised by Mario Carneiro, 11-Dec-2016.) |
Ref | Expression |
---|---|
r19.37.1 |
Ref | Expression |
---|---|
r19.37 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | r19.35 3084 | . 2 | |
2 | r19.37.1 | . . . 4 | |
3 | ax-1 6 | . . . 4 | |
4 | 2, 3 | ralrimi 2957 | . . 3 |
5 | 4 | imim1i 63 | . 2 |
6 | 1, 5 | sylbi 207 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wnf 1708 wcel 1990 wral 2912 wrex 2913 |
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-12 2047 |
This theorem depends on definitions: df-bi 197 df-an 386 df-ex 1705 df-nf 1710 df-ral 2917 df-rex 2918 |
This theorem is referenced by: r19.37v 3087 ss2iundf 37951 |
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