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Mirrors > Home > ILE Home > Th. List > pm3.21 | GIF version |
Description: Join antecedents with conjunction. Theorem *3.21 of [WhiteheadRussell] p. 111. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
pm3.21 | ⊢ (𝜑 → (𝜓 → (𝜓 ∧ 𝜑))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm3.2 138 | . 2 ⊢ (𝜓 → (𝜑 → (𝜓 ∧ 𝜑))) | |
2 | 1 | com12 30 | 1 ⊢ (𝜑 → (𝜓 → (𝜓 ∧ 𝜑))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia3 107 |
This theorem is referenced by: pm3.22 263 iba 298 ancr 319 anc2r 326 pm5.31 346 xoranor 1372 19.41h 1678 19.41 1679 ltsopr 7551 bj-findis 13979 |
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