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Mirrors > Home > MPE Home > Th. List > dfifp2 | Structured version Visualization version Unicode version |
Description: Alternate definition of the conditional operator for propositions. The value of if- is "if then , and if not then ." This is the definition used in Section II.24 of [Church] p. 129 (Definition D12 page 132) (see comment of df-ifp 1013). (Contributed by BJ, 22-Jun-2019.) |
Ref | Expression |
---|---|
dfifp2 | if- |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ifp 1013 | . 2 if- | |
2 | cases2 993 | . 2 | |
3 | 1, 2 | bitri 264 | 1 if- |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 196 wo 383 wa 384 if-wif 1012 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-ifp 1013 |
This theorem is referenced by: dfifp3 1015 dfifp5 1017 ifpn 1022 ifpimpda 1028 ifpbi2 37811 ifpbi3 37812 ifpbi23 37817 ifpbi1 37822 ifpbi12 37833 ifpbi13 37834 ifpbi123 37835 ifpimimb 37849 ifpororb 37850 ifpbibib 37855 frege54cor0a 38157 |
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