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Mirrors > Home > ILE Home > Th. List > mpgbir | Unicode version |
Description: Modus ponens on biconditional combined with generalization. (Contributed by NM, 24-May-1994.) (Proof shortened by Stefan Allan, 28-Oct-2008.) |
Ref | Expression |
---|---|
mpgbir.1 | |
mpgbir.2 |
Ref | Expression |
---|---|
mpgbir |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpgbir.2 | . . 3 | |
2 | 1 | ax-gen 1442 | . 2 |
3 | mpgbir.1 | . 2 | |
4 | 2, 3 | mpbir 145 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wal 1346 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-gen 1442 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: nfi 1455 cvjust 2165 eqriv 2167 abbi2i 2285 nfci 2302 abid2f 2338 rgen 2523 ssriv 3151 ss2abi 3219 nel0 3436 ssmin 3850 intab 3860 iunab 3919 iinab 3934 sndisj 3985 disjxsn 3987 intid 4209 fr0 4336 zfregfr 4558 peano1 4578 relssi 4702 dm0 4825 dmi 4826 funopabeq 5234 isarep2 5285 fvopab3ig 5570 opabex 5720 acexmid 5852 finomni 7116 dfuzi 9322 fzodisj 10134 fzouzdisj 10136 bdelir 13882 |
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